Warm-Up Please log into your calculator to answer the warm- up question

Writing the Equation of a Circle Essential Question: How do you write the equation of a circle? What does each piece in the equation represent? Demonstrated in writing in summary at conclusion of notes.

Equation of a Circle in Standard Form: (x - h)2 + (y – k)2 = r2 If you are given the center and the radius, just plug in. The x-coordinate of the center is h, the y-coordinate of the center is k, and the radius is r.

Example: Write the equation (in standard form) for the circle described. a) center: (-1, 3) b) center: (0, 7) radius: 3 radius: 5

If you are given the center and a point on the circle, use the distance formula (𝑑= ( 𝑥 1 − 𝑥 2 ) 2 + ( 𝑦 1 − 𝑦 2 ) 2 ) to find the radius and then plug in.

Example: Write the equation (in standard form) for the circle with center at (1, -2) and that contains the point (-1, 1).

Example: Write the equation (in standard form) for the circle with center at (3, 6) and that contains the point (8, 1).

If you are given the coordinates of two points on the circle, find the midpoint of the two points using the formula 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 . This point is the center. Then choose one of the original points, it does not matter which one, and plug in.

Example: Write the equation (in standard form) of the circle that contains the points (0,2) and (4, 0).

Example: Write the equation (in standard form) of the circle that contains the points (1,-1) and (-5, 7).

Homework: Writing the equation of a circle worksheet problems 1 - 7

Warm-Up Please log into your calculator to answer the warm- up question

If you are asked to show that a point is on a circle, find the length of the radius using the distance formula (𝑑= ( 𝑥 1 − 𝑥 2 ) 2 + ( 𝑦 1 − 𝑦 2 ) 2 ) and then find the distance from the center to the given point and show they are the same. If you are given the equation of the circle you can plug in the coordinates of the point and show that the equation is satisfied.

Example: Prove or disprove that the point (1, 3 ) lies on the circle centered at the origin and containing the point (0, 2).

A circle drawn on a coordinate plane has center (–1, 2) and contains the point (-1,0).  Hanorah wants to prove that the point (𝟎, 𝟑 +𝟐) lies on the circle. Which of the following steps could Hanorah take?  Select all that apply.

If you are given the equation of a circle in general form (x2 + y2 + cx + dy + e = 0) and asked to convert to standard form you must complete the square twice, once for the x’s and once for the y’s.

Example: Convert x2 + y2 – 4x + 10y + 20 = 0 into standard form.

Example: Convert x2 + y2 – 4x – 6y + 8 = 0 into standard form.

Homework: Writing the equation of a circle worksheet problems 8 - 10