Enter guardian's email if under 13 years old

Teacher {teacherName} invited you to be the guardian of {studentName}.

Full Name

Do not use your real name

If you do not have an account yet, you will receive a verification link at

If you do not have an account yet, you will receive a verification link at the provided email.

Please click the link to confirm your email.

Grab a coffee, you deserve it! I'll take care of everything.

Change title

This content was not found or is private.

Warning

Title

Enter new title

Title cannot be empty

Change content cover

Test your knowledge with this interactive crossword game

Crossword

You will chat with a personalized chatbot to help you learn and review the content

You will chat with a personalized chatbot to help you learn and review the content. Remember: your teacher may see your interactions.

Activity with AI

If selected, the content will be visible to everyone and other teachers will be able to view and download it.

Public content

Topic

Test your knowledge with this interactive flashcard game

Play Flashcards

Flashcards

How can we enhance this content?

Help Teachy improve!

This is a preview of your tutor. Click "Edit" to interact with it and adapt as needed.

Questions asked to Lara

Subscription Required

Test your knowledge with this interactive word search game

Play Word Search

Word Search

IARA TIP

Connect with other teachers, receive and share materials, tips, training, and much more!

Join a community of teachers directly on WhatsApp

Log in to Teachy to comment on this content

Teachy uses cookies to enhance your browsing experience, analyze site traffic, and improve the overall performance of our website. You can manage your preferences or accept all cookies.

We use cookies

We use browser cookies that are essential for the proper functioning of the site. For example, we store your data collection preferences so we can respect them if you return to our site. You can disable these cookies in your browser settings, but if you do, the site may not function as intended.

Essentials

The Facebook Pixel integration allows you to measure and optimize the performance of your ads on Facebook.

Facebook Pixel

Google Analytics 4 (GA4) is Google's new analytics property that you can use for both websites and apps. GA4 incorporates machine learning to automatically reveal useful insights and provide a comprehensive understanding of your customers across devices and platforms.

Google Analytics

The LinkedIn Insight Tag integration allows you to track user conversions on your website and measure the performance of your ads on LinkedIn.

LinkedIn Insight Tag

Mixpanel is a business analytics tool that allows you to track user activity on web and mobile applications.

Mixpanel

Posthog is an analytics tool that captures all user session data on your site. It allows you to replay individual user sessions to identify issues and enhance the user experience.

Posthog

The Tiktok Pixel integration allows you to measure and optimize the performance of your ads on Tiktok.

Tiktok Pixel

Teachy uses data collected by cookies and JavaScript libraries to enhance your browsing experience, analyze site traffic, and improve the overall performance of our website.

Cookie Preferences

The table below describes how we use this data by category. To opt out of a data collection category, uncheck the option and save your preferences.

Reinvent teaching

Materials

Audiences

Resources

Hi, Renan! I want to bring Teachy to my school. Can you help me?

Plans

Error

Evaluation Criteria

Develop a {essayType} essay on the topic: **{theme}**

Essay Proposal

Essay on {theme}

This link will open an external website that is not controlled by Teachy. We cannot guarantee the content or security of this site. Do you wish to continue?

You are leaving Teachy

Creating your Assignment...

Magically creating your lesson...

Pre-lesson (Preparation)

During Lesson (Learning)

Post-lesson (Application)

During Lesson

Post-lesson (Homework/Retention)

Post-lesson (Review)

First contact with the content

In-depth exploration

Retention

Practical

Theoretical support

Test preparation

Introduction to Content

Real-life Application

Edit this content with AI to make it perfect.

Unsupported Browser

Get full access to dozens of subjects and hundreds of materials on Teachy!

Didn't find what you were looking for?

Why are Teachy's Assignment Generators the <mostComplete>most complete available</mostComplete>?

Why are Teachy's book chapters the <mostComplete>most complete available</mostComplete>?

Why are Teachy's Lesson Plans the <mostComplete>most complete available</mostComplete>?

Why are Teachy's lesson plans the <mostComplete>most complete available</mostComplete>?

Why are Teachy's projects and activities the <mostComplete>most complete available</mostComplete>?

Why are Teachy's Question Banks the <mostComplete>most complete available</mostComplete>?

Why are Teachy's slides the <mostComplete>most complete available</mostComplete>?

Why are Teachy's summaries the <mostComplete>most complete available</mostComplete>?

Access our lesson plans from anywhere, at any time, simplifying your lesson planning and preparation.

Convenient access:

Our lesson plans are crafted by education experts and cover all subjects. These materials are aligned with the national curriculum to ensure quality teaching.

Comprehensive content:

Our lesson plans are thoughtfully designed to foster student engagement, from elementary to high school, and maximize their learning.

Enhanced student performance:

With just a few clicks, you can find and adapt lesson plans tailored to your needs and those of your class.

Effortless customization:

Stop wasting time creating lesson plans from scratch. Our ready-to-use lesson plans save you time so you can focus on what truly matters: teaching.

Save time:

Quick and easy access to quality slides from anywhere, making your lesson preparation more efficient and less burdensome.

Our slides are created by education specialists and cover a wide range of subjects, providing an effective visual tool for teaching.

Our slides are thoughtfully designed to engage students and facilitate understanding of concepts, helping them achieve better academic outcomes.

Tailor slides to meet the specific needs of your class. Our platform simplifies the adaptation of visual content for various educational levels.

Cut down on preparation time with our ready-to-use slides, allowing you to focus more on teaching and less on material preparation.

Log in with your account to see the <t>full content</t> for free

Log in with your account to see the <t>full presentation</t> for free

and unlock over 60 AI Tools created for over 5 million educators.

Create personalized slides with AI for free

I can generate slides, activities, summaries, and 60+ types of materials. That's right, no sleepless nights here :)

Need customized slides for your lessons?

You need to be a registered teacher to view the answer sheet

Hello :)

Pengantar Geometri Analitik & Irisan Kerucut; Lingkaran: Persamaan dan Garis Singgung; Parabola, Elips, dan Hiperbola; Aplikasi Irisan Kerucut di Dunia Nyata; Strategi Pemecahan Masalah & Diskusi

Geometri Analitik: Irisan Kerucut

Matematika

Geometri Analitik: Irisan Kerucut

Menjelajahi hubungan aljabar dan geometri melalui irisan kerucut.

Agenda

• Pengantar Geometri Analitik & Irisan Kerucut

• Lingkaran: Persamaan dan Garis Singgung

• Parabola, Elips, dan Hiperbola

• Aplikasi Irisan Kerucut di Dunia Nyata

• Strategi Pemecahan Masalah & Diskusi

Pengantar Geometri Analitik

Geometri analitik adalah cabang matematika yang menjembatani aljabar dan geometri. Ia memungkinkan kita memvisualisasikan persamaan matematika sebagai bentuk geometris. Ini dilakukan melalui penggunaan sistem koordinat Kartesius.

Memahami fungsi melalui grafik matematika.

Kerucut coklat tunggal di atas permukaan datar, latar belakang hijau.

Irisan Kerucut: Konsep Dasar

• Irisan Kerucut: Kurva hasil irisan bidang datar dengan kerucut ganda.

• Lingkaran &amp; Elips: Bidang memotong satu kerucut (lingkaran tegak lurus sumbu).

• Parabola: Bidang memotong satu kerucut, sejajar garis pelukis.

• Hiperbola: Bidang memotong kedua kerucut ganda.

Persamaan Lingkaran Baku

Persamaan lingkaran baku berpusat di (0,0) adalah x² + y² = r². Jika pusatnya di (a,b), persamaannya menjadi (x-a)² + (y-b)² = r². Dari persamaan (x-3)² + (y+2)² = 25, pusatnya adalah (3,-2) dan jari-jarinya 5.

Memahami lingkaran: pusat, jari-jari, dan luasnya.

Rumus luas lingkaran: A = πr² untuk pemahaman geometri.

Menentukan Elemen Lingkaran

• Dari bentuk baku: (x-h)²+(y-k)²=r².

• Pusat (h,k) dan jari-jari (r) langsung terlihat.

• Dari bentuk umum: x²+y²+Ax+By+C=0.

• Pusat (-A/2, -B/2); jari-jari √((-A/2)²+(-B/2)²-C).

Langkah Analisis Awal

Peran Diskriminan (D)

Untuk menentukan kedudukan garis terhadap lingkaran, langkah pertama adalah mensubstitusikan persamaan garis (misalnya y = mx + c) ke dalam persamaan lingkaran. Hasil substitusi ini akan membentuk sebuah persamaan kuadrat dalam satu variabel, baik x maupun y. Persamaan kuadrat inilah yang menjadi dasar analisis selanjutnya.

Setelah mendapatkan persamaan kuadrat, nilai diskriminan (D = b² - 4ac) akan menentukan kedudukan garis terhadap lingkaran. Jika D &gt; 0, garis memotong lingkaran di dua titik berbeda. Jika D = 0, garis menyinggung lingkaran di satu titik. Apabila D &lt; 0, garis tidak memotong maupun menyinggung lingkaran.

Persamaan Garis Singgung Lingkaran (Titik)

Persamaan garis singgung lingkaran yang melalui titik (x₁, y₁) pada lingkaran dapat ditentukan dengan mensubstitusikan titik tersebut ke dalam bentuk umum persamaan lingkaran. Untuk lingkaran berpusat di (0,0) dengan jari-jari r, rumusnya adalah x₁x + y₁y = r². Jika pusatnya (a,b), maka (x₁-a)(x-a) + (y₁-b)(y-b) = r².

Grafik fungsi tangen y = tan(x) dengan asimtot vertikal.

Persamaan Garis Singgung Lingkaran (Gradien)

Kita dapat menentukan persamaan garis singgung lingkaran jika gradien (m) garis tersebut diketahui. Untuk lingkaran berpusat di (0,0) dengan jari-jari r, rumusnya adalah y = mx ± r√(1+m²). Jika pusat lingkaran di (a,b), rumusnya menjadi (y-b) = m(x-a) ± r√(1+m²).

Grafik fungsi tangen y = tan(x/2) dengan asimtot vertikal.

Teorema Sudut Keliling: Memahami Lingkaran dalam Geometri.

Memahami fungsi kuadrat: f(x) = ax² + bx + c.

Parabola: Persamaan &amp; Elemen

• Persamaan standar: (x-h)²=4p(y-k) atau (y-k)²=4p(x-h).

• Titik Puncak (h,k): Titik balik kurva parabola.

• Titik Fokus: Jarak 'p' dari puncak, pada sumbu simetri.

• Direktris: Garis tegak lurus sumbu simetri, jarak 'p'.

Geometri Analitik: Irisan Kerucut

Pengantar Geometri Analitik & Irisan Kerucut; Lingkaran: Persamaan dan Garis Singgung; Parabola, Elips, dan Hiperbola; Aplikasi Irisan Kerucut di Dunia Nyata; Strategi Pemecahan Masalah & Diskusi

People who viewed this slide also liked...