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The sum of the slopes of the tangents to...

The sum of the slopes of the tangents to the parabola `y^(2)=8x` drawn from the point (-2,3) is

A

-1

B

-2

C

-3/2

D

2

Text Solution

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The correct Answer is:
C
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The product of the slopes of the tangents to the parabola y^(2)=4x drawn from the point (2,3) is

A : The sum and product of the slopes of the tangents to the parabola y^(2)=8x drawn form the point (-2,3) are -3/2,-1 . R : If m_(1),m_(2) are the slopes of the tangents of the parabola y^(2) =4ax through P (x_(1),y_(1)) then m_(1)+m_(2)=y_(1)//x_(1),m_(1)m_(2)=a//x_(1) .

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The sum of the slopes of the tangents to the ellipse x^(2)//9+y^(2)//4=1 drawn from the point (6, -2) is

The product of the slopes of the tangents to the ellipse 2x^(2)+3y^(2)=6 drawn from the point (1, 2) is

The product of the slopes of the tangents to the ellipse 2x^(2)+3y^(2)=6 drawn from the point (1,2) is

The sum and product of the slopes of the tangents to the hyperbola 2x^(2) -3y^(2) =6 drawn form the point (-1,1) are

The sum of the slopes of the tangents to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 drawn from the point (6, -2) is

Assertion (A) : the sum and product of the slopes of the tangents to the ellipse (x^2)/(9)+(y^2)/(4)=1 drawn from the points (6,-2) are -8/9 ,1. Reason(R): if m_(1),m_(2) are the slopes of the tangents through (x_(1),y_(1)) of the ellipse, then m_(1)+m_(2)=(2x_(1).y_(1))/(x_(1)^(2)-a^(2)) m_(1).m_(2)=(y_(1)^(2)-b^(2))/(x_(1)^(2)-a^(2))

DIPTI PUBLICATION ( AP EAMET)-PARABOLA-EXERCISE 1 A
  1. The two parabolas y^(2)=4x and x^(2)=4y intersect at a point P whose...

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  2. If the common tangent of the circle x^(2)+y^(2)=c^(2) and the parabola...

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  3. The sum of the slopes of the tangents to the parabola y^(2)=8x drawn f...

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  4. The product of the slopes of the tangents to the parabola y^(2)=4x dra...

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  5. The slope of tangents drawn from a point (4,10) to the parabola y^(2)=...

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  6. The point of intersection of the tangents at the ends of latusrectum o...

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  7. The locus of the point of intersection of perpendicular tangents to th...

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  8. If two tangents drawn from a point P to the parabola y^(2)=4x are at r...

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  9. The tangents at the ends of a focal chord of a parabola y^(2)=4ax int...

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  10. The locus of the point of intersectio of the perpendicular tangents to...

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  11. The locus of the point of intersection of two tangents to the parabola...

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  12. The locus of the point of intersection of two tangents to the parabola...

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  13. The locus of the point of intersection of two tangents to the parabola...

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  14. The locus of the point of intersection of two tangents to the parabola...

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  15. The locus of the point of intersection of two tangents to the parabola...

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  16. The locus of point of intersection of tangents to y^(2) = 4ax which in...

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  17. Two straight lines are perpendicular to each other. One of them touche...

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  18. The locus of the point of intersection of tangents to the parabola y^(...

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  19. The equation of a tangent to the parabola y^(2) =8x is y =x+2 . The po...

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  20. Through the vertex O of the parabola y^(2)=4ax a perpendicular is draw...

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