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  • AB is a chord of the parabola with vertex at A BC is drawn perpendi

AB is a chord of the parabola \mathrm{y^2=4 a x} with vertex at A BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the axis of the parabola is

Option: 1

\mathrm{a}


Option: 2

\mathrm{2a}


Option: 3

\mathrm{4a}


Option: 4

\mathrm{\frac{a}{2}}


Answers (1)

best_answer

A is (0,0). Let point on the parabola be \mathrm{\left(x_1, y_1\right).}

\mathrm{ \Rightarrow \quad y_1^2=4 a x_1 }

In  \mathrm{ \triangle A B D,} we have

\mathrm{ \tan \theta=\frac{y_1}{x_1} }
In \mathrm{\triangle B C D,}
\mathrm{ \begin{aligned} \tan (90-\theta) & =\frac{y_1}{C D} \\\\ \Rightarrow \quad C D=y_1 \tan \theta & =\frac{y_1^2}{x_1} \\\\ & =\frac{4 a x_1}{x_1}=4 a \end{aligned} }

Posted by

Ritika Kankaria

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