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  • The line is a tangent to the hyperbola <img alt="\mathrm{7 x^2-5

The line \mathrm{21 x+5 y=116} is a tangent to the hyperbola \mathrm{7 x^2-5 y^2=232.} Its point of contact is

Option: 1

(-6,-2)


Option: 2

(6,2)


Option: 3

(6,-2)


Option: 4

(-6,2)


Answers (1)

The line \mathrm{21 x+5 y=116} is a tangent to \mathrm{7 x^2-5 y^2=232.}

If \mathrm{P\left(x_1, y_1\right)} is the point of contact, then \mathrm{S_1=0.}

\mathrm{\Rightarrow 7 x_1 x-5 y_1 y=232}. It is same as \mathrm{21 x+5 y=116}

\mathrm{ \begin{aligned} & \therefore \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} }

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Kshitij

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