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  • Find the length of the line-segment joining the vertex of the parabola y^2 = 4ax and a point on the parabola where the line-segment makes an angle q to the x-axis.

Q: Find the length of the line-segment joining the vertex of the parabola y2 = 4ax and a point on the parabola where the line-segment makes an angle \theta to the x-axis.

Answers (1)

Let the point on the parabola be P (x1,y1)  

Slope of OP=\tan \theta =\frac{y_{1}}{x_{1}}

y_{1}^{2}=4ax_{1}

x_{1}=\frac{4a}{\tan ^{2}\theta }

OP=\frac{4a \sec \theta }{\tan ^{2}\theta }= \frac{4a \cos \theta }{\sin^{2}\theta }

 

Posted by

infoexpert22

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