Question

Find the center radius of the circle x^2 + y^2 + 3/4x + 5/3y - 1/2 = 0

Answer 1

(-3/8, -5/6) ; √(769)/24 Choice B

Explanation:

Convert this to standard form ( (x - a)^2 + (y - b)^2 = r^2 where a,b is the centre and r = radius) :-

x^2 + y^2 + 3/4 x + 5/3 y - 1/2 = 0

x^2 + 3/4 x + y^2 + 5/3 y = 1/2

(x + 3/8)^2 - (3/8)^2 + ( y + 5/6)^2 - (5/6)^2 = 1/2

( x + 3/8)^2 + ( y + 5/6)^2 = 1/2 + 9/64 + 25/36

( x + 3/8)^2 + ( y + 5/6)^2 = 769/576

So comparing this with the above standard from :-

center = (-3/8, -5/6) and radius is sqrt (769/576) = sqrt 769 / 24