Find the values of a and b ....on circles ?

Vinay sipani

if the equation of common chord of the circles

3x² + 3y²- 2a²x + 6y + 6 = 0 and 2x² + 2y²- 4x + by - 4 = 0 is 4x - 3y - 24 , find a and b ?

Bipin Dubey

Circles are : $S1 : x^{2}+y^{2}-\frac{2a^{2}}{3}x+2y+2=0$ and $S2 : x^{2}+y^{2}-2x+\frac{b}{2}y-2=0$

Common chord is S1-S2 = 0 => $(\frac{2a^{2}}{3}-2)x+(\frac{b}{2}-2)y-4=0$ which is to be compared with 4x-3y-24=0

$\frac{(\frac{2a^{2}}{3}-2)}{4}=\frac{(\frac{b}{2}-2)}{-3}=\frac{-4}{-24}$

$\Rightarrow b=3, \: a=\pm 2$