1 / 11

Equations of Circles

Learn how to derive and write the equation of circles with given centers and radii. Explore examples step by step. Practice mathematical reasoning and problem-solving skills.

hkrause
Download Presentation

Equations of Circles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Equations of Circles Concept 44

  2. Content Standards G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Mathematical Practices 2 Reason abstractly and quantitatively. 7 Look for and make use of structure. CCSS

  3. Concept

  4. 1. Write the equation of the circle with a center at (3, –3) and a radius of 6. (x – h)2 + (y – k)2 = r2 Equation of circle (x – 3)2 + (y – (–3))2 = 62 Substitution (x – 3)2 + (y + 3)2 = 36 Simplify. Answer:(x – 3)2 + (y + 3)2 = 36 Example 1

  5. 2. Write the equation of the circle graphed to the right. The center is at (1, 3) and the radius is 2. (x – h)2 + (y – k)2 = r2 Equation of circle (x – 1)2 + (y – 3)2 = 22 Substitution (x – 1)2 + (y – 3)2 = 4 Simplify. Answer:(x – 1)2 + (y – 3)2 = 4 Example 1

  6. 3. Write the equation of the circle with a center at (2, –4) and a radius of 4. A.(x – 2)2 + (y + 4)2 = 4 B.(x + 2)2 + (y – 4)2 = 4 C.(x – 2)2 + (y + 4)2 = 16 D.(x + 2)2 + (y – 4)2 = 16 Example 1

  7. 4. Write the equation of the circle graphed to the right. A.x2 + (y + 3)2 = 3 B.x2 + (y – 3)2 = 3 C.x2 + (y + 3)2 = 9 D.x2 + (y – 3)2 = 9 Example 1

  8. 5. List the center and radius length of the circle with the formula x2 + (y + 3)2 = 9. x2 + (y + 3)2 = 9 (x – 0) 2 + (y – -3)2 = (3) 2 (0, -3) R = 3

  9. 6. List the center and radius length of the circle with the formula (x + 3)2 + (y – 2)2 = 18 (x – -3)2 + (y – 2)2 = 18

  10. 7. Write the equation of the circle that has its center at (–3, –2) and passes through (1, –2). (x – h)2 + (y – k)2 = r2 (x + 3)2 + (y + 2)2 = r2 Plug it in (1 + 3)2 + (-2 + 2)2 = r2 (4)2 + (0)2 = r2 16 = r2 Answer:(x + 3)2 + (y + 2)2 = 16 Example 2

  11. 8. Write the equation of the circle that has its center at (–1, 0) and passes through (3, 0). (x – h)2 + (y – k)2 = r2 (x + 1)2 + (y + 0)2 = r2 Plug it in (3 + 1)2 + (0 + 0)2 = r2 (4)2 + (0)2 = r2 16 = r2 Answer:(x + 1)2 + y2 = 16 Example 2

More Related