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A line of slope lambda(0 lt lambda lt 1)...

A line of slope `lambda(0 lt lambda lt 1)` touches the parabola `y+3x^2=0` at `P`. If `S` is the focus and `M` is the foot of the perpendicular of directrix from `P` , then `tan/_M P S`

A

`2lamda`

B

`(2lamda)/(-1+lamda^(2))`

C

`(1-lamda^(2))/(1+lamda^(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
(2)
Slope of line `=lamda=tantheta`
`:." "tan(angleMPS)=tan((pi)/(2)-theta)=tan(pi-2theta)`
`=-tan2theta=(2lamda)/(lamda^(2)-1)`
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  4. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

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  5. If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

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  8. At what point on the parabola y^2=4x the normal makes equal angle with...

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  13. The radius of the circle touching the parabola y^2=x at (1, 1) and hav...

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  14. If two different tangents of y^2=4x are the normals to x^2=4b y , then...

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  16. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

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  17. min[(x1-x^2)^2+(3+sqrt(1-x1 2)-sqrt(4x2))],AAx1,x2 in R , is 4sqrt(5)...

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  18. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

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  19. Normals A O ,AA1a n dAA2 are drawn to the parabola y^2=8x from the poi...

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