Question

7. x2 + y2-4x-8y-45 = 0

Answer 1

The given equation of circle is x 2 + y 2 −4x−8y−45=0

The formula for the equation of circle is given by,

( x−h ) 2 + ( y−k ) 2 = r 2 (1)

Where, h and k denotes the center of the circle and r denotes the radius of the circle.

Equation (1) can be written as,

( x 2 −4x )+( y 2 −8y )−45=0

Now add and subtract 4 and 16 to make complete squares within parenthesis we get,

( x 2 −4x+4 )+( y 2 −8y+16 )−45−4−16=0 ( x−2 ) 2 + ( y−4 ) 2 =65 ( x−2 ) 2 + ( y−4 ) 2 = ( 65 ) 2

Comparing equation (1) and (2) we get h=2,k=4 and r = 65

Thus the center of the circle is (2,4) and radius of the circle is 65