Question

X2

What is the radius of the circle with the equation X
- 4x + y2 + 2y – 20 = 0;
Enter the answer in the box.

Answer 1

The radius of the circle 'r' = 5

Equation of the circle

(x - 2 )² + (y+1)² = (5)²

center of the circle ( h,k) = (2 , -1) , 'r' = 5

Explanation:

Step(i):-

Given circle is x² - 4 x + y² + 2 y - 20 =0

x² - 2(2) x + (2)²-(2)²+ y² + 2 y(1) +(1)²-(1)² - 20 = 0

We know that

(a+b)² = a²+2 a b+b²

(a-b)² = a² -2 a b+b²

⇒(x - 2 )² - 4 + (y+1)² -21 =0

⇒ (x - 2 )² + (y+1)² = 25

Step(ii):-

Equation of the circle form

( x- h)² + (y -k)² = r²

Given circle (x - 2 )² + (y+1)² = (5)²

center of the circle ( h,k) = (2 , -1)

radius of the circle 'r' = 5