Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaTangent to ParabolaMedium2 minQB

MathematicsMediumsingle choice

The locus point of intersection of tangents to the parabola $y^{2} = 4 ax$ , the angle between them being always 45° is

Answer:

Solution:

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

$m^{2} x - m y + a = 0$

$m_{1} + m_{2} = \frac{y}{x}$

$m_{1} m_{2} = \frac{a}{x}$

$tan 4 5^{\circ} = \frac{m _{1} - m _{2}}{1 + m _{1} m _{2}}$

$(\frac{y}{x})^{2} - 4 (\frac{a}{x}) = (1 + \frac{a}{x})^{2}$

$x^{2} - y^{2} + 6 a x + a^{2} = 0$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Tangent to Parabola

⏱ 2mℹ️ Source: QB

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