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The line 2x+y+lamda=0 is a normal to the...

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

A

12

B

-12

C

24

D

-24

Text Solution

Verified by Experts

The correct Answer is:
C
(3) y=mx+c is a normal to `y^(2)=4ax` if `c=-2am-am^(3)`,
`y=-2x-lamda` (Given normal)
`:." "m=-2,a=-2`
`or-lamda=-2an-am^(3)=-2(-2)(-2)-(-2)(-2)^(3)=-24`
`orlamda=24`
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CENGAGE-PARABOLA-Exercise (Single)
  1. If the tangents and normals at the extremities of a focal chord of a ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. From a point (sintheta,costheta), if three normals can be drawn to the...

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  16. If the normals at P(t(1))andQ(t(2)) on the parabola meet on the same p...

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  17. If the normals to the parabola y^2=4a x at P meets the curve again at ...

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  18. PQ is a normal chord of the parabola y^2= 4ax at P,A being the vertex ...

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  19. P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8...

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  20. Normals at two points (x1y1)a n d(x2, y2) of the parabola y^2=4x meet ...

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