Find the equation of the tangents to the hyperbola $4 x^{2} - 9 y^{2} = 36$ passing through $(3, 0)$

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Solution

Equation of hyperbola $4 x^{2} - 9 y^{2} = 36$
Slope of tangent is $8 x - 18 y \frac{d y}{d x} = 0 4 x - 9 y \frac{d y}{d x} = 0 \frac{d y}{d x} = \frac{4 x}{9 y} {\frac{d y}{d x} ∣ ∣ ∣}_{(3, 0)} = \frac{12}{0}$
Equation of tangent is $y - 0 = \frac{12}{0} (x - 3) x - 3 = 0 x = 3$

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