Q. The equation of the tangent to the conic $x^{2} - y^{2} - 8x + 2y + 11 = 0$ at $(2,\ 1)$ is
A) $x + 2 = 0$
B) $2x + 1 = 0$
C) $x + y + 1 = 0$
D) $x - 2 = 0$
Explanation
(d)
Equation of the tangent at $\left( x_{1,}y_{1} \right)$ is
$xx_{1} - yy_{1} - 4\left( x + x_{1} \right) + \left( y + y_{1} \right) + 11 = 0$
Put $x_{1} = 2\$and $y_{1} = 1$, we get$\$
$2x - y - 4(x + 2) + (y + 1) + 11 = 0$
$\Rightarrow \ - 2x - 8 + 12 = 0$
$\Rightarrow \ \ \ x - 2 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.