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The mirror image of the parabola y^(2)=4...

The mirror image of the parabola `y^(2)=4x` in the tangent to the parabola at the point (1,2) is

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The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

If a straight line passing through the focus of the parabola y^(2) = 4ax intersectts the parabola at the points (x_(1), y_(1)) and (x_(2), y_(2)) , then prove that x_(1)x_(2)=a^(2) .

If a straight line pasing through the focus of the parabola y^(2) = 4ax intersects the parabola at the points (x_(1), y_(1)) and (x_(2) , y_(2)) then prove that y_(1)y_(2)+4x_(1)x_(2)=0 .

If a straight line passing through the focus of the parabola x ^(2) =4ay intersects the parabola at the points (x_(1) , y_(1)) and (x_(2), y_(2)) then the value of x_(1)x_(2) is-

Let PQ be a focal chord of the parabola y^2 = 4ax The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0 . Length of chord PQ is

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

The area of the figure bounded by the parabola (y-2)^(2)=x-1, the tangent to it at the point with the ordinate y=3, and the x-axis is

Find the equation of the tangent to the parabola y^2=4a x at the point (a t^2,\ 2a t) .

Prove that the chord y-xsqrt(2)+4asqrt(2)=0 is a normal chord of the parabola y^2=4a x . Also find the point on the parabola when the given chord is normal to the parabola.

Let the curve C be the mirror image of the parabola y^2 = 4x with respect to the line x+y+4=0 . If A and B are the points of intersection of C with the line y=-5 , then the distance between A and B is

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If two chords drawn from the point A(4,4) to the parabola x^2=4y are b...

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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. The mirror image of the parabola y^(2)=4x in the tangent to the parabo...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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