Question

What is the equation of a circle with center (–7, –2) and radius 4?

Answer 1

(x + 7)² + (y + 2)² = 16

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) = (- 7, - 2) and r = 4

(x - (- 7))² + (y - (- 2))² = 4²

(x + 7)² + (y + 2)² = 16 ← equation of circle

Answer 2

x2 + y2 + 14x + 4y -37 =0

Explanation:

Equation of a circle in standard form can be written as,

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

Here h, k are the coordinates of the centre and r is the radius as centre,

(-7,-2) and r=4

Substituting the values as given in the questions

(x-(-7))2 + (y-(-2))2 = (4)2

Simplying it further,

(x+7)2 + (y+2)2 = 16

x2 +14x+ 49 + y2+ 4y + 4= 16

Equation required

x2 + y2 + 14x + 4y -37 =0

Therefore, the required equation of the circle.