Question

Write the standard equation for the circle center (-6,8) that passes through (0,0)

Answer 1

D

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

here (h, k) = (- 6, - 8), thus

(x + 6)² + (y + 8)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 6, - 8) and (x₂, y₂ ) = (0, 0)

r =
`√((0+6)^2+(0+8)^2)` =
`√(36+64)` =
`√(100)` = 10

Hence

(x + 6)² + (y + 8)² = 100 → D