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If y=m1x+c and y=m2x+c are two tangents ...

If `y=m_1x+c` and `y=m_2x+c` are two tangents to the parabola `y^2+4a(x+a)=0` , then

A

`m_(1)+m_(2)=0`

B

`1+m_(1)+m_(2)=0`

C

`m_(1)m_(2)-1=0`

D

`1+m_(1)m_(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) Tangent `y=m_(1)x+candy=m_(2)x+c` intersect at (0,c) which lies on the directrix of the given parabola.
Hence, the tangents are perpendicular, for which `m_(1)m_(2)=-1`.
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CENGAGE-PARABOLA-Exercise (Single)
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  2. y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tan...

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  3. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+a)=0 ...

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  4. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

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  5. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

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  6. Radius of the circle that passes through the origin and touches the ...

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  7. The mirror image of the parabola y^2=4x in the tangent to the parab...

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

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

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  10. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

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

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

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

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

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  15. If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is ...

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  16. about to only mathematics

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

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

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

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

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