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Find the locus of the middle points of the chords of the parabola `y^2=4a x` which subtend a right angle at the vertex of the parabola.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. An equilateral triangle is inscribed in the parabola y^2=4a x , such t...

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  2. M is the foot of the perpendicular from a point P on a parabola y^2=4a...

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

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  4. A quadrilateral is inscribed in a parabola y^2=4a x and three of its ...

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  5. A right-angled triangle A B C is inscribed in parabola y^2=4x , where ...

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  6. Let there be two parabolas y^2=4a x and y^2=-4b x (where a!=ba n da ,b...

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  7. The equation of aparabola is y^2=4xdotP(1,3) and Q(1,1) are two poin...

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  8. A P is perpendicular to P B , where A is the vertex of the parabola y^...

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  9. Find the value of P such that the vertex of y=x^2+2px+13 is 4 units ab...

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  10. The point (a ,2a) is an interior point of the region bounded by the pa...

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  11. Find the point where the line x+y=6 is a normal to the parabola y^2=8x...

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  12. Find the equation of the tangent to the parabola 9x^2+12 x+18 y-14=0 w...

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  13. Find the angle between the tangents drawn to y^2=4x , where it is inte...

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  14. How many distinct real tangents that can be drawn from (0,-2) to th...

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  15. Find the angle at which the parabolas y^2=4x and x^2=32 y intersect.

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  16. If the tangents at the points Pa n dQ on the parabola y^2=4a x meet at...

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  17. The tangents to the parabola y^2=4x at the points (1, 2) and (4,4) mee...

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  18. From an external point P , a pair of tangents is drawn to the parabola...

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  19. If the line x+y=a touches the parabola y=x-x^2, then find the value of...

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  20. Find the slopes of the tangents to the parabola y^2=8x which are norma...

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