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If the tangents and normal at the extremities of focal chord of a parabola intersect at the extremities of a focal chord of a parabola intersect at `(x_(1),y_(1))and(x_(2),y_(2))`, respectively, then

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Prove that the normal at the extermities of a focal chord of a parabola intersect at right angles.

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_1,y_1) and (x_2,y_2), respectively, then (a) x_1=y_2 (b) x_1=y_1 (c) y_1=y_2 (d) x_2=y_1

Prove that the least focal chord of a parabola is the latus rectum .

Prove that the least focal chord of a parabola is its latus rectum .

Prove that the sum of the reciprocals of the segments of any focal chord of a parabola is constant .

If the extremitied of a focal chord of the parabola y^2=4ax be (at_1^2,2at_1) and (at_2^2,2at_2) ,show that t_1t_2=-1

Length of the shortest normal chord of the parabola y^2=4ax is

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

Show that the product of the ordinates of the ends of a focal chord of the parabola y^(2) = 4ax is constant .

Show that the sum of the reciprocals of the segments of any focal chord of a parabola y^2=4ax is constant.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. The mirror image of the parabola y^(2)=4x in the tangent to the parabo...

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

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  3. If the tangents and normal at the extremities of focal chord of a para...

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

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  5. If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...

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  6. y=x+2 is any tangent to the parabola y^(2)=8x. The point P on this tan...

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  7. Two parabola have the same focus. If their directrices are the x-and t...

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  8. The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...

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  9. The length of the chord of the parabola y^(2)=x which is bisected at t...

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  10. The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the l...

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  11. A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ ...

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  12. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

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

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  14. Let S be the focus of y^2=4x and a point P be moving on the curve s...

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  15. If a!=0 and the line 2b x+3c y+4d=0 passes through the points of ...

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  16. If y(1),y(2),andy(3) are the ordinates of the vertices of a triangle i...

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  17. The circle x^(2)+y^(2)+2lamdax=0,lamdainR, touches the parabola y^(2)=...

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  18. If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , the...

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  19. Parabolas y^(2)=4a(x-c(1))andx^(2)=4a(y-c(2)), where c(1) and c(2) are...

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  20. A circle touches the x-axis and also touches the circle with centre (0...

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