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Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaTangent to ParabolaEasy2 minQB

MathematicsEasyinteger

Two tangents are drawn from point $(1, 4)$ to the parabola $y^{2} = 4 x$ . Angle between these tangents is $\frac{π}{K}$ then $K =$

Answer:

Solution:

The line $y = m x + \frac{1}{m}$ is tangent to the parabola $y^{2} = 4 x$ .

$\Rightarrow y^{2} = m + \frac{1}{m} \Rightarrow m^{2} - 4 m + 1 = 0 m_{1} + m_{2} = 4, m_{1} m_{2} = 1 tan θ = \frac{m _{1} - m _{2}}{1 + m _{1} m _{2}} = 3 θ = \frac{π}{3}$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Tangent to Parabola

⏱ 2mℹ️ Source: QB

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