Given a circle with center (-6,9) and a point on the circle (-3,5)

Question

a) Write an equation of the circle in standard form.

b) Using your equation in part A, determine if the coordinate (-2,6)

is on the circle. Justify your answer.

Answer 1

a)

The center (0,0) and the radius r then

The equation of the circle : x² + y² = r²

The center (h,k) and the radius r then

The equation of the circle in standard form : (x - h)² + (y - k)² = r².

Answer 2

a)

The center (h,k) and the radius r then

The equation of the circle in standard form : (x - h)² + (y - k)² = r²

The center (-6 ,9) and the point on the circle (-3,5)

Substitute h = -6 , k = 9 in the above form : (x - (-6))² + (y - 9)² = r²

Substitute the point (-3,5) in the above form : (-3+ 6)² + (5 - 9)² = r²

                                                                                 3² + (-4)² = r²

                                                                                        25 = r²

                                                                                         r² = 25.

The equation of the circle in standard form : (x +6))² + (y - 9)² = 25

                                                                                  x² + y² + 12x  - 18y + 92 = 0.

Answer 3

b)

The center (h,k) and the radius r then

The equation of the circle in standard form : (x - h)² + (y - k)² = r²

The center (-6 ,9) and the point on the circle (-2,6)

Substitute h = -6 , k = 9 in the above form : (x - (-6))² + (y - 9)² = r²

Substitute the point (-3,5) in the above form : (-2+ 6)² + (6 - 9)² = r²

                                                                                 4² + (-3)² = r²

                                                                                        25 = r²

                                                                                         r² = 25.

The equation of the circle in standard form : (x +6))² + (y - 9)² = 25

                                                                                  x² + y² + 12x  - 18y + 92 = 0.