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Three normals are drawn from the point (...

Three normals are drawn from the point (c,0) to the curve `y^2=x`. Show that c must be greater than `(1)/(2)`. One normal is always the X-axis. Find c for which the other two normals are perpendicular to each other.

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A DAS GUPTA-Parabola-EXERCISE
  1. Three normals are drawn from the point (c,0) to the curve y^2=x. Show...

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  2. Find the equation of the parabola, if the focus is at (-6,-6) and the...

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  3. Prove that the equation y^(2)+2ax+2by+c=0 represents a parabola whose ...

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  4. Prove that the equation y^2-2y+8x-23=0reprsents a parabola and find it...

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  5. If (a^2, a -2) be a point interior to the region of the parabola y^2...

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  6. Show that the tangents at the extremities of any focal chord of a par...

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  7. The orthocenter of a triangle formed by 3 tangents to a parabola y^2=4...

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  8. Tangents are drawn from any point on the line x+4a=0 to the parabola y...

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  9. Prove that the area of triangle formed by the tangents to the parabola...

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  10. Points A, B, C lie on the parabola y^2=4ax The tangents to the parabol...

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  11. If P, Q, R are three points on a parabola y^2=4ax whose ordinates are ...

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  12. Prove that any three tangents to a parabola whose slopes are in harmon...

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

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  14. Find the equation of the chord to the parabola y^2=4axwhose middle poi...

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  15. Prove that the normal chord to a parabola at the point whose ordinate ...

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  16. Show that the area formed by the normals to y^2=4ax at the points t1,t...

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  17. P & Q are the points of contact of the tangents drawn from the point T...

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  18. For what values of 'a' will the tangents drawn to the parabola y^2 = 4...

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

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

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

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