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Obj. 60 Circles in the Coordinate Plane
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Circles
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Nov. 3 Coordinate Equation Of A Circle
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Equation of a circle
Equation of a circlevhughes5 Here are some things you did well and could improve on:
WWW:
- You explained the key concepts around writing the equation of a circle clearly and concisely. Breaking it down step-by-step makes it easy to understand.
- Providing examples with worked solutions is very helpful for reinforcement. The visual diagrams additionally aid comprehension.
- Giving practice problems for students to try on their own, along with answers, allows for application of the material.
EBI:
- Some of the text could be formatted for easier reading (e.g. consistent formatting of equations).
- Adding brief summaries or recaps after sections of explanation may aid retention.
- Providing guidance on common errors
Lesson plan in mathematics
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Final lesson plan in Math (4A's Approach)
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2. The lesson includes an opening prayer and greeting, reviewing the previous lesson on parallelograms, a hands-on activity to discover the triangle area formula, worked examples, and a short quiz as homework.
3. Key points covered are that the area of a triangle is one-half the area of the rectangle or parallelogram upon which it is based, and the formula for calculating triangle area is 1/2 x base x height.
Circle : Basic concept
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- The radius is the fixed distance from the center point to any point on the circle.
- A chord connects any two points on a circle. A diameter passes through the center and divides the circle into two equal halves.
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Circle questions
- 1. QUESTIONS 1- Sketch the circle x2 + y2 = 4. Find the center and radius first. -The equation is in the form x2 + y2 = r2, so we have a circle, center (0, 0) with radius r = √4 = 2
- 2. 2- Sketch the circle (x − 2)2 + (y − 3)2 = 16 Find the center and radius first. -The equation is in the form (x − h)2 + (y − k)2 = r2, so we have a circle with centre at (2, 3) and the radius is r = √16 = 4.
- 3. 3- Sketch the circle (x + 4)2 + (y − 5)2 = 36 -We have a circle with centre at (-4, 5) and the radius is r = √36 = 6.
- 4. 4. Find the equation of the circle with centre (3/2, -2) and radius 5/2. -Centre (3/2, -2) radius 5/2
- 5. 5- Find the points of intersection of the circle x2 + y2 − x − 3y = 0 with the line y = x − 1. -We solve the 2 equations simultaneously by substituting the expression y = x -1 into the expression We have:
- 6. So we see that the solutions for x are x = 1 or x = 2. This gives the corresponding y-vales of y = 0 and y = 1. So the points of intersection are at: (1, 0) and (2, 1). We can see that our answer is correct in a sketch of the situation: