Question

The center of a circle is at (2, −5) and its radius is 12.

What is the equation of the circle?


(x−2)2+(y+5)2=144

(x+2)2+(y−5)2=24

(x−2)2+(y+5)2=24

(x+2)2+(y−5)2=144

Answer 1

The equation of the circle is (x - 2)² + (y + 5)² = 144 ⇒ A

Explanation:

The form of the equation of the circle is (x - h)² + (y - k)² = r², where

• r is the radius of the circle

• h, k are the coordinates of the center of the circle

Let us solve the question

∵ The center of the circle is at (2, -5)

→ From the rule above

∴ h = 2 and k = -5

∵ The radius of the circle is 12

∴ r = 12

→ Substitute the values of r, h, and k in the form of the equation above

∵ (x - 2)² + (y - -5)² = (12)²

∴ (x - 2)² + (y + 5)² = 144

∴ The equation of the circle is (x - 2)² + (y + 5)² = 144