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Show that the locus of the middle points of normal chords of the parabola `y^2=4ax` is

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The focus of the parabola y^2= 4ax is :

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.

Find the locus of the middle points of equal chords of a circle.

The directrix of the parabola y^2=4ax is :

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

Find the locus of the middle points of the parallel chords of a circle.

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 a parabola. Find the vertex of this parabola.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Prove that the equation of the parabola whose vertex and focus are on ...

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  2. Find the focus of the parabola x^2=4y

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  3. Show that the locus of the middle points of normal chords of the parab...

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  4. If any tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cuts off inter...

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  5. The vertices of a quadrilateral are situated at foci and the extremiti...

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  6. Find the equation of the hyperbola whose foci are (8, 3), (0, 3) and w...

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  7. Find the slope of the line passing through the points : (3, - 2) and...

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  8. The slope of the line passing through the points (3,-2) and (-1,4) is:

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  9. Slope of the line passing through the points (3, -2) and (3, 4) is:

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  10. If the equation of a circle is: x^2 + y^2 + 8x -10y+8=0, then its cent...

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  11. The centre of the circle x^(2)+y^(2)-6x+4y-1=0 is

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  12. If the equation of a circle is: x^2 + y^2-4x-8y -45 =0, then its centr...

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  13. The centre of the circle x^2+y^2+8x+10y-8=0 is:

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  14. The radius of the circle : x^2 + y^2-8x + 10y- 12 =0 is:

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  15. The directrix of the parabola y^2=4ax is :

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  16. The directrix of the parabola y^(2) + 4x + 3 = 0 is :

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  17. The focus of the parabola y^2= 4ax is :

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  18. The vertex of the parabola y^2= 4ax is

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  19. The focus of the parabola y = 2x^2 + x is

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  20. The foci of the ellipse 9x^2 +4y^2 =36 are

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