Q88 / 180 · COMEDK 2017 · Mathematics
The line $21 x+5 y=116$ is a tangent to the hyperbola $7 x^{2}-5 y^{2}=232$. Its point of contact is
- A$(-6,-2)$
- B$(6,2)$
- Correct answerC$(6,-2)$
- D$(-6,2)$
Solution
The line $21 x+5 y=116$ is a tangent to $7 x^{2}-5 y^{2}=232$. If $P\left(x_{1}, y_{1}\right)$ is the point of contact, then $S_{1}=0$.
$\begin{aligned}
&\Rightarrow 7 x_{1} x-5 y_{1} y=232 \text { It is same as } 21 x+5 y=116 \\
&\therefore \quad \frac{7 x_{1}}{21}=-\frac{5 y_{1}}{5}=\frac{232}{116}=2 \\
&\therefore \quad x_{1}=6, y_{1}=-2 . \text { So, } P \text { is }(6,-2) .
\end{aligned}$
Hence, the correct answer is option: 'C'.