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If the chord x+2 y+\lambda=0 subtends a right angle at the vertex of the parabola x^2=6 y, then \lambda = .........

Option: 1

0


Option: 2

12


 


Option: 3

-12

 


Option: 4

10


Answers (1)

best_answer

The chord is AB. The combined equation of OA and OB is obtained by making (2) homogeneous with (1)

So                                   x^2=6 y\left(\frac{x+2 y}{-\lambda}\right)

\Rightarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \quad \lambda x^2+6 x y+12 y^2=0

By the hypothesis, OA perpendicular to OB, So coefficient of x^2+ coefficient of y^2=0

Or                                  \lambda+12=0 \Rightarrow \lambda=-12

Posted by

Divya Prakash Singh

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