Find the equations of tangents to the hyperbola $x^{2} - 4 y^{2} = 36$ which are perpendicular to the line $x - y + 4 = 0$ :

y = - x \pm 3 \sqrt{3}

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y = - x \pm 3 \sqrt{2}

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y = - x \pm 3 \sqrt{4}

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None of these

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Solution

The correct option is A $y = - x \pm 3 \sqrt{3}$
Slop of the given line $x - y + 4 = 0$ is 1 and hence slope of tangent perpendicualr to it is $- 1 = m .$
Also $a^{2} = 36, b^{2} = 9.$
Hence the tangent is $y = m x \pm \sqrt{a^{2} m^{2} - b^{2}}$ or $y = - x \pm 3 \sqrt{3} .$

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Similar questions

x^{2} - 4 y^{2} = 36

x - y + 4 = 0

Find the equation of the tangent to the hyperbola $x^{2} - 4 y^{2} = 36$ which is perpendicular to the line $x - y + 4 = 0$

3 x^{2} - 4 y^{2} = 12

y = x^{3} + 2 x - 4

x + 14 y + 3 = 0.

Find the equation of the tangents to the curve $y = x^{3} + 2 x - 4$ , which are perpendicular to the line x + 14y + 3 = 0.

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