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

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Prove that the the middle points of the normal chords of the parabola y^(2)=4ax is on the curve (y^(2))/(2a)+(4a^(3))/(y^(2))=x-2a

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

Find the length of the normal chord of a parabola y^2 = 4x , which makes an angle 45^@ with its axes.

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 ordinate of end of any chord of a system of paralel chords of the parabola y^(2)=4ax 1 is constant.

The locus of the midpoints of all chords of the parabola y^(2) = 4ax through its vertex is another parabola with directrix is

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

The length of the common chord of the parabolas y^(2)=x and x^(2)=y is

Find the length of the common chord of the parabola y^2=4(x+3) and the circle x^2+y^2+4x=0 .

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

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. t 1 and  t 2 are two points on the parabola y^...

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  2. Tangent and normal are drawn at the point P-=(16 ,16) of the parabola ...

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

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  4. The line x-y=1 intersect the parabola y^(2)=4x at A and B. Normals at ...

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  5. If normals drawn from a point P(h,k) to the parabola y^(2)=4ax, then t...

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  6. If x+y=k is normal to y^2=12 x , then k is (a)3 (b) 9 (c) -9 (d) -3

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  7. An equilateral triangle is inscribed in the parabola y^(2)=4ax, such...

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  8. Evaluate, min[(x1-x2)^2+(5+sqrt(1-x1^2)-sqrt(4x2))^2],AAx1,x2 in R , ...

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  9. The equation of the directrix of the parabola y^2+4y+4x+2=0 is (a)x=-1...

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  10. The equation of the common tangent touching the circle (x-3)^2+y^2=9 ...

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

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  12. The focal chord of y^(2)=16x is tangent to (x-6)^(2)+y^(2)=2. Then t...

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  13. The locus of the midpoint of the segment joining the focus to a moving...

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  14. Show that the curve whose parametric coordinates are x=t^(2)+t+l,y=t^(...

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  15. Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Stateme...

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  16. Consider a circle with its centre lying on the focus of the parabola, ...

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  17. Normal drawn to y^2=4a x at the points where it is intersected by the...

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

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

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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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