Question

Write the equation of a circle whose center is (-4,8) and passes through the point (-2,-1).(Hint... use the distance formula to find the radius)

A : (x + 4)2 + (y - 8)2 = 85

B: (x + 2)2 + (y + 1)2 = 85

C: (x + 2)2 + (y + 1)2 = 40

D: (x - 4)2 + (y - 8)2 = 40

Answer 1

Let the equation of the circle be (x-h)²+(y-k)²=r² .........(i)

Given,

Center (h,k) = (-4,8)

The circle passes through the point (-2,1)

Now,

Radius, r = √(-4+2)²+(8+1)² = √4+81 = √85

So, r² = 85

Now,

(i)⇒ (x+4)²+(y-8)² = 85

So, the answer is A.