Question

Consider the equation of the circle.

x^2 − 14x + y^2 = 15
What is the length of the radius of the circle defined by the given equation?

Answer 1

radius = 8

Explanation:

NOTE ================================

EQUATION OF A CIRCLE with center (a , b) and radius r :

(x - a)² + (y-b)² = r²

……………………………………………

x² − 14x + y² = 15

⇔ x² − 2×7x + 7² − 7² + y² = 15

⇔ x² − 2×7x + 49 − 49 + y² = 15

⇔ (x - 7)² − 49 + y² = 15

⇔ (x - 7)² + y² = 15 + 49

⇔ (x - 7)² + y² = 64

⇔ (x - 7)² + y² = 8²

Then radius of the circle is 8.