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Prove that the length of the intercept o...

Prove that the length of the intercept on the normal at the point `P(a t^2,2a t)` of the parabola `y^2=4a x` made by the circle described on the line joining the focus and `P` as diameter is `asqrt(1+t^2)` .

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A DAS GUPTA-Parabola-EXERCISE
  1. For what values of 'a' will the tangents drawn to the parabola y^2 = 4...

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  2. Find the centre and radius of the smaller of the two circles that touc...

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  3. Prove that the length of the intercept on the normal at the point P(a ...

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  4. Prove that the locus of the middle pointsof chords of the parabolay^2=...

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  5. Prove that the locus of a point, which moves so that its distance from...

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  6. 5. The locus of point of intersection of two tangents to the parabola ...

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  7. Find the locus of the intersection of normals to the parabolay^2=4axat...

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  8. Find the locus of the point of intersection of those normals to the pa...

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  9. Find the locus of point of intersection of tangent to the parabola y^2...

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  10. Find the locus of the middle points of the chords of the parabola y^2=...

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  11. Show that the locus of points such that two of the three normals drawn...

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  12. Prove that the locus of the point of intersection of the normals at th...

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  13. Find the locus of the middle points of the chords of the parabola y^2=...

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  14. If two tangents to the parabola y^2=4ax from a point P make angles ...

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  15. Locus of the feet of the perpendiculars drawn from vertex of the parab...

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  16. If the focus =(2,3)and directrix is x+y=1 then the equation of the par...

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  17. The line x+y+1=0touches the parabola y^2=kx if k=.

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  18. If the normals to the parabola y^2=4a x at the ends of the latus rectu...

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  19. Write the length of het chord of the parabola y^2=4a x which passes th...

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  20. Find the condition that the line x cosalpha + y sin alpha=p touches th...

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