Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaChordsEasy2 minQB

MathematicsEasysingle choice

The length of the chord of the parabola $x^{2} = 4 y$ passing through the vertex and having slope $cot α$ is

Answer:

Solution:

Let $A =$ vertex, $AP =$ chord of $x^{2} = 4 y$ such that slope of AP is $cot α$

Let $P = (2 t, t^{2})$

Slope of $A P = \frac{1}{2} \Rightarrow cot α = \frac{1}{2} \Rightarrow t = 2 cot α$

Now, $A P = 4 t^{2} + t^{4} = t 4 + t^{2}$

$= 4 cot α cosec α$

$= 4 cos α \cdot cos e^{2} α$

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Chords

⏱ 2mℹ️ Source: QB

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