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Prove that the locus of the point of int...

Prove that the locus of the point of intersection of the normals at the ends of a system of parallel chords of a parabola is a straight line which is a normal to the curve.

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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.

Prove that the normal at the extermities of a focal chord of a parabola intersect at right angles.

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the locus of the point of intersection of two normals to a parabo...

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  2. P(t(1))andQ(t(2)) are points t(1)andt(2) on the parabola y^(2)=4ax. ...

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

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  4. Find the number of distinct normals that can be drawn from (-2,1) to t...

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  5. If the line passing through the focus S of the parabola y=ax^(2)+bx+c ...

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  6. If a focal chord of y^(2)=4ax makes an angle alphain[pi//4,pi//2] with...

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  7. Find the length of normal chord which subtends an angle of 90^(@) at t...

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  8. Find the locus of the point of intersection of the normals at the end ...

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  9. If AB is a focal chord of x^(2)-2x+y-2=0 whose focus is S and AS=l(1),...

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  10. A circle is drawn to pass through the extermities of the latus rcetum ...

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  11. Circle drawn having its diameter equal to the focal distance of any po...

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  12. If the length of a focal chord of the parabola y^2=4a x at a distance ...

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  13. Find the equation of the parabola whose focus is S(-1,1) and directrix...

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  14. If x^2 + y^2 = log(xy) , find dy/dx .

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  15. If (2,-8) is an end of a focal chord of the parabola y^(2)=32x, then f...

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

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  17. Find the minimum distance between the curves y^2=4x and x^2+y^2-12 x+3...

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  18. If y=2x+3 is a tangent to the parabola y^(2)=24x, then find its distan...

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  19. Three normals to y^2=4x pass through the point (15, 12). Show that one...

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  20. Find the locus of the point from which the two tangents grawn to the p...

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