If the line $3 x-m y+5=0$ is a tangent to the hyperbola $3 x^2-4 y^2=300$ then the square of the $Y-$ intercept made by this tangent line is

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Aicharya · Accepted Answer

$3 x^2-4 y^2=300$ $ \frac{x^2}{100}-\frac{y^2}{75}=1 $ and $3 x-m y+5=0 \Rightarrow y=\frac{3}{m} x+\frac{5}{m}$ Now, for condition of tangents: $ \begin{aligned} & \mathrm{c}^2=\mathrm{a}^2 \mathrm{~m}^2-\mathrm{n}^2 \Rightarrow \frac{25}{\mathrm{~m}^2}=100 	imes \frac{9}{\mathrm{~m}^2}-75 \ & \Rightarrow \mathrm{m}^2=\frac{35}{3} \end{aligned} $ Square of $y$ - intercept of $x$-radius $ \mathrm{c}=\frac{25}{\mathrm{~m}^2}=25 	imes \frac{3}{35}=\frac{15}{7} $

If the line $3 x-m y+5=0$ is a tangent to the hyperbola $3 x^2-4 y^2=300$ then the square of the $Y-$…

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