Q. The value of $k$ so that $x^{2} + y^{2} + kx + 4y + 2 = 0$ and $2\left( x^{2} + y^{2} \right) - 4x - 3y + k = 0$ cut orthogonally, is
A) $\frac{10}{3}$
B) $- \frac{8}{3}$
C) $- \frac{10}{3}$
D) $\frac{8}{3}$
Explanation
(c)
Here, $g_{1} = \frac{k}{2},\ \ f_{1} = 2,\ \ \ c_{1} = 2$
And $g_{2} = - 1,\ \ \ f_{2} = - \frac{3}{4},\ \ \ c_{2} = \frac{k}{2}$
$\because$ Given circles cut orthogonally
$\therefore\ \ \ 2 \times \frac{k}{2} \times ( - 1) + 2 \times 2 \times \left( - \frac{3}{4} \right) = 2 + \frac{k}{2}$
$\Rightarrow \ \ - k - 3 = 2 + \frac{k}{2}\ \ \Rightarrow \ \ k = \frac{- 10}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.