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  • Find the equation of normal to the parabola  at the ends of latus rec

Find the equation of normal to the parabola \mathrm{y^2=4 a x } at the ends of latus rectum. If the normals again meet the parabola at \mathrm{Q} and \mathrm{Q^{\prime}}, then \mathrm{Q^{\prime}=}

Option: 1

4a


Option: 2

8a


Option: 3

12a


Option: 4

14a


Answers (1)

best_answer

The ends of the latus rectum are \mathrm{(a, 2 a)} and \mathrm{(a,-2 a)} at which equations of normals respectively are \mathrm{y=-x+3 a} and \mathrm{y=x-3 a.}
If normal is drawn at \mathrm{\left(\mathrm{am}^2,-2 \mathrm{am}\right)}, then it intersects the parabola again at \mathrm{\left(\mathrm{am}_1{ }^2,-2 \mathrm{am}_1\right),}
where \mathrm{m_1=-m-\frac{2}{m}}

Hence \mathrm{Q \equiv(9 a,-6 a)} and \mathrm{ Q^{\prime} \equiv(9 a, 6 a)}. Hence \mathrm{ Q Q^{\prime}=12 a.}

Posted by

Pankaj

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