Question

Find the centre and radius of the circle (1) X2+y2+6x+8y-96=0 And
(2) 3x2+3y2-5x-6y+4=0.

Answer 1

Answer:

x²+y²+6x+8y-96=0

or, (x²+6x+9)+(y²+8y+16)= 96+9+16=121

or, (x+3)²+(y+4)²=11²

centre= (-3,-4) , radius=11

3x²+3y²-5x -6y+4=0

or, x²+y²-(5/3)x -2y +(4/3)=0

or, {x²-(5/3)x+(25/36)}+(y²-2y+1)= (25/36)+1-(4/3)

or, {x-(5/6)}²+(y-1)²= 13/36 = (√13/6)²

centre= (5/6, 1) , radius= √13/6