Question

Write the standard form of the equation of the circle with center (-5,-7) that passes through the point (7,5).

Answer 1

(x + 5)² + (y + 7)² = 288

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)

r =
`√((7+5)^2+(5+7)^2)` =
`√(12^2+12^2)` =
`√(288)`

Hence

(x - (- 5))² + (y - (- 7))² = (
`√(288)`)², that is

(x + 5)² + (y + 7)² = 288