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Show that the locus of a point that divi...

Show that the locus of a point that divides a chord of slope 2 of the parabola `y^2=4x` internally in the ratio `1:2` is parabola. Find the vertex of this parabola.

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CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Three normals are drawn from the point (c, 0) to the curve y^2 = x. Sh...

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  2. Find the equation of the normal to the curve x^(2) = 4y which passes t...

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  3. Show that the locus of a point that divides a chord of slope 2 of the ...

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  4. Points A, B, C lie on the parabola y^2=4ax The tangents to the parabol...

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  5. If the focus of the parabola x^2-k y+3=0 is (0,2), then a values of k ...

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  6. Let P be a point whose coordinates differ by unity and the point does ...

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  7. Statement 1: The line x-y-5=0 cannot be normal to the parabola (5x-15)...

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  8. Consider the parabola y^2=12 x Column I, Column II Equation of ta...

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  9. If the tangent at the point P(2,4) to the parabola y^(2)=8x meets the ...

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  10. Let P be the family of parabolas y=x^2+p x+q ,(q!=0), whose graphs cut...

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  11. If normal at point P on the parabola y^2=4a x ,(a >0), meets it again ...

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  12. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

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  13. The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with...

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  14. Tangent is drawn at any point (p ,q) on the parabola y^2=4a xdot Tange...

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  15. The equation of the directrix of the parabola with vertex at the origi...

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  16. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

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  17. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

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  18. Statement 1: If the parabola y^2=4a x and the circle x^2+y^2+2b x=0 to...

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  19. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then th...

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  20. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

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