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Prove that on the axis of any parabola t...

Prove that on the axis of any parabola there is a certain point 'k' which has the property that, if a chord PQ of parabola be drawn through it then `1/(PK)^2+1/(QK)^2` is the same for all positions of the chord.

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The correct Answer is:
`1/(4a^2)`
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ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that on the axis of any parabola there is a certain point 'k' wh...

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  2. Tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y...

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  3. let P be the point (1, 0) and Q be a point on the locus y^2= 8x. The l...

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  4. The axis of parabola is along the line y=x and the distance of its ver...

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  5. The equations of the common tangents to the parabola y = x^2 and y=-...

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  6. The locus of the vertices of the family of parabolas y =[a^3x^2]/3 + [...

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  7. Angle between the tangents to the curve y=x^2-5x+6 at the points (2,0)...

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  8. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  9. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  10. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  11. Statement I The curve y = x^2/2+x+1 is symmetric with respect to the l...

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  12. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+...

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  13. Consider the two curves C1 ; y^2 = 4x, C2 : x^2 + y^2 - 6x + 1 = 0 the...

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  14. A parabola has the origin as its focus and the line x=2 as the directr...

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  15. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

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  16. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

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  17. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

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  18. Consider the parabola y^2 = 8x. Let Delta1 be the area of the triangle...

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  19. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

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  20. Let (x,y) be any point on the parabola y^2 = 4x. Let P be the point t...

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  21. The shortest distance between line y-x=1 and curve x=y^2 is

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