Question

Which equation describes a circle with center (4,−7) and radius 9? A (x−4)2+(y+7)2=81 B (x+4)2+(y−7)2=81 C (x−4)2+(y+7)2=9 D (x+4)2+(y−7)2=9

Answer 1

A. (x - 4)² + (y + 7)² = 81

Explanation:

The general equation for a circle is given by the formula;

x² + y² + 2hx + 2ky + c = 0 ......equation 1.

Where the center is C(-h, -k)

Also, the standard form of the equation of a circle is;

(x - h)² + (y - k)² = r² ......equation 2.

Where;

• h and k represents the coordinates of the centre.
• r represents the radius of the circle.

Given the following data;

h = 4

k = -7

r = 9

Substituting into eqn 2, we have;

(x - 4)² + (y - {-7})² = 9²

Simplifying further, we have;

(x - 4)² + (y + 7)² = 81