What will be the equation of tangent at the point $P (10, 8)$ on the rectangular hyperbola $\frac{x^{2}}{36} - \frac{y^{2}}{36} = 1 ?$

5 x + 4 y = 18

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5 x - 4 y = 18

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8 x - 5 y = 18

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4 x - 5 y = 18

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Solution

The correct option is B $5 x - 4 y = 18$
Given: Rectangular hyperbola $\frac{x^{2}}{36} - \frac{y^{2}}{36} = 1$ ; Point $P (10, 8)$

To Find: Equation of tangent

We know that the equation of tangent at $P (x_{1}, y_{1})$ on rectangular hyperbola is: $x x_{1} - y y_{1} = a^{2}$

From the given data, we have $a^{2} = 36, x_{1} = 10, y_{1} = 8$

Substituting all the values in the equation of tangent.

$\Rightarrow 10 x - 8 y = 36$

$\Rightarrow 5 x - 4 y = 18$

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