Question

If the radical centre of $x^2+y^2-4x+2y+3=0,x^2+y^2-x+4y+4=0$ and $x^2+y^2+2gx+5+7=0$ is $\left(-1,1\right)$ then $g=$

• A. $-3$
• B. $3$
• C. $-3/2$
• D. $5/2$

Answer 1

The correct option is D $5/2$

Let $S_1=x^2+y^2-4x+2y+3$

$S_2=x^2+y^2-x+4y+4$

$S_3=x^2+y^2+2gx+5y+7$

radical centre=$(-1,1)$

Finding Radical axes,

$S_2-S_1=3x+2y+1=0------\left(1\right)$

$S_3-S_2=(2g-1)x+y+3=0------\left(2\right)$

Solving 1 &2,eliminating variable y,we get,

$x=\frac{5}{5-4g}$

Now,

$\frac{5}{5-4g}=(-1)$

$=>g=\frac{5}{2}$