Question

8. x2 + y2-8x + 10y-12=0

Answer 1

The given equation of circle is x 2 + y 2 −8x+10y−12=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 −8x )+( y 2 +10y )−12=0

Now add and subtract 16 and 25 to make complete squares within parenthesis we get,

( x 2 −8x+16 )+( y 2 +10y+25 )−12−25−16=0 ( x−4 ) 2 + ( y+5 ) 2 =53 ( x−4 ) 2 + ( y+5 ) 2 = ( 53 ) 2

Comparing equation (1) and (2) we get h=4,k=5 and r = 53

Thus the center of the circle is (4,−5) and radius of the circle is 53