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A line of slope lambda(0<lambda<1) touch...

A line of slope `lambda(0

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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CENGAGE-PARABOLA-Exercise (Single)
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  2. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

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  3. A line of slope lambda(0<lambda<1) touches the parabola y+3x^2=0 at Pd...

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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^2,26),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

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  6. The minimum area of circle which touches the parabolas y=x^(2)+1andy^(...

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  7. If the tangents and normals at the extremities of a focal chord of a ...

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

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  9. The line 2x+y+lamda=0 is a normal to the parabola y^(2)=-8x, is lamda=

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  10. If two normals to a parabola y^2 = 4ax intersect at right angles then ...

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  11. The equation of the line that passes through (10 ,-1) and is perpendic...

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  12. Tongent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

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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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  15. Maximum number of common normals of y^2=4ax and x^2=4by is

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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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  20. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

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