Question

X2

Answer 1

Answer:

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

Step-by-step 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