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Two parabolas have the same vertex and e...

Two parabolas have the same vertex and equal lengh of latus rectum such that their axes are at right angle. Prove that the common tangents touch each at the end of latus rectum.

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Common tangent to the parabola touches the parabola cut `L'= (-2a,a)`
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AAKASH SERIES-PARABOLA-SOLVED EXAMPLES
  1. The normals from (P,0) are drawn to the parabola y^(2) = 8x, one of th...

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  2. Show that the locus of point of intersection of perpendicular tangents...

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  3. Show that the equation of the common tangent to the circle x^(2) + y^(...

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  4. The locus of the foot of the perpendicular from the focus to the tange...

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  5. Show that straight line 7x+6y=13 is a tangent to the parabola y^(2)-7x...

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  6. Find the condition for the line y=mx+c to be a tangent to the parabola...

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  7. If a chord of the parabola y^(2) = 4ax touches the parabola y^(2) = 4b...

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

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  9. Show that the focal chord of the parabola y^(2)=4ax, which makes an an...

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  10. Show that semi latus rectum of the parabola y^(2) =4ax is the harmonic...

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

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

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  13. Prove that the point on the parabola y^(2) = 4a ( a gt 0 nearest to th...

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

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  15. The sum of the ordinates of two points on y(2)=4ax is equal to the sum...

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  16. Prove that the portion of the tangent intercepted between the point of...

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  17. Prove that the radius of the circle whose centre is (-4,0) and which c...

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  18. A triangle ABC of area Delta is inserted in the parabola y^(2) =4ax su...

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

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

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