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Prove that the point on the parabola y^(...

Prove that the point on the parabola `y^(2) = 4ax (a gt0)` nearest to the focus is its vertex.

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AAKASH SERIES-PARABOLA-SOLVED EXAMPLES
  1. If a chord of lhe parabola y^(2) = 4ax touches the parabola y^(2) = 4b...

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  2. Prove that two parabolas y(2)=4ax "and" x^(2)=4by intersect (other tha...

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  3. Prove that the point on the parabola y^(2) = 4ax (a gt0) nearest to th...

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  4. Prove that the locus of point of intersection of two perpendicular nor...

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  5. If ((1)/(2),2) is one extermity of a focalchord of the parabola y^(2)=...

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  6. Two parabolas have the same vertex and equal lengh of latus rectum su...

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  7. Prove that the portion or the tangent intercepted,between the point of...

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  8. Prove that the circle on a focal radius of a parabola, as diameter tou...

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  9. Prove that the orthocentre of the triangle formed by any three tangent...

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  10. The conic represented by 2x^(2) -12xy +23y^(2) -4x -28y -48 =0 is

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  11. Find the conic represented by the equation sqrt( ax) + sqrt( by) = 1?

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  12. If the equation x^(2) - y^(2) - 2x+2y+lambda =0 represents a degenerat...

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  13. If the equation x^(2) + y^(2) - 2x -2y+ c=0 represents an empty set th...

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  14. If the equation of conic 2x^(2) + xy+3y^(2) - 3x+ 5y + lambda =0 repre...

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  15. For what value of lambda the equation of conic 2xy+4x-6y+ lambda=0 rep...

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  16. Find the centre of the conic 14x^(2) - 4xy + 11y^(2) - 44x - 58y +71=0

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  17. Find the coordinates of the vertex and focus and the equations of the ...

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  18. Find the coordinates of the vertex and focus and the equations of the ...

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  19. Find the coordinates of the vertex and focus and the equations of the ...

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  20. Find the vertex, focus, equation of directrix and axis, of parabolas ...

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