Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaMiscellaneous/MixedMedium2 min

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The locus point of intersection of tangents to the parabola $y^{2} = 4 a x$ , the angle between them being always $4 5^{\circ}$ is

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Answer:

Solution:

Equation of tangent is $y = m x + \frac{a}{m}$

$\Rightarrow m^{2} x - m y + a = 0 \Rightarrow m_{1} + m_{2} = \frac{y}{x}, m_{1} m_{2} = \frac{a}{x} tan 4 5^{\circ} = \frac{m _{1} - m _{2}}{1 + m _{1} m _{2}} \Rightarrow (\frac{y}{x})^{2} - 4 (\frac{a}{x}) = (1 + \frac{a}{x})^{2} \Rightarrow x^{2} - y^{2} + 6 a x + a^{2} = 0$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Miscellaneous/Mixed

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