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Let P be a point on the parabola y^(2) -...

Let P be a point on the parabola `y^(2) - 2y - 4x+5=0`, such that the tangent on the parabola at P intersects the directrix at point Q. Let R be the point that divides the line segment PQ externally in the ratio `1/2` : 1. Find the locus of R.

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The correct Answer is:
`2(y - 1)^(2)(x - 2) = (3x - 4)^(2)`
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MOTION-PARABOLA-EXERCISE - III
  1. Find the equation of tangents of the parabola y^2=12 x , which passes ...

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  2. From vertex O ofthe parabola y^2=4ax perpendicular is drawn at a tange...

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  3. Let P be a point on the parabola y^(2) - 2y - 4x+5=0, such that the ta...

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  4. Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex...

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  5. Show that the normals at the points (4a, 4a) & at the upper end of t...

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  6. In the parabola y^(2) = 4ax, the tangent at the point P, whose absciss...

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  7. Prove that the locus of the middle point of portion of a normal to y^(...

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

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  9. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

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  10. Prove that, the normal to y^(2) = 12x at (3,6) meets the parabola agai...

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

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  12. A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to th...

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  13. Show that the normals at two suitable distinct real points on the para...

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  14. Let S is the focus of the parabola y^(2) = 4ax and X the foot of the d...

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  15. Prove that the parabola y^(2) = 16x and the circle x^(2) + y^(2) - 40x...

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  16. .Find the equation ofthe circle which passes through the focus ofthe p...

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  17. A fixed parabola y^(2) = 4ax touches a variable parabola. Find the equ...

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  18. Show that an infinite number of triangles can be inscribed in either o...

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  19. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

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  20. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

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