Question

1) find the center and radius of the given equation of the circle
x2+y2-24x-48y+7=0​

Answer 1

Answer:

center (12,24)

radius = 26.7

Answer 2

Answer:

Step-by-step explanation

Sol:   The equation of the circle is x2+ y2+2gx+2fy+c=0

    Now given equation is x2+y2-24x-48y+7=0

  Compare the co-efficients

⇒  2gx = -24  ;  2fy = -48

    - g = -12     ; -f = -24

Centre of the Circle = (-g,-f) ⇒ -g = -12 , -f= -24

                           ⇒ g=12 ; f=24 ( ∵ On both the sides minus get cancelled )    Radius of the circle = √ g2+f2-c ( Under root g square + f square - c )

  ⇒   √12 square + 24 square - 7 = √144 + 576 -7 = √720-7=√713  

       ∴ Centre =  (12 , 24)  & Radius = √713 .