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Prove that the locus of middle points of...

Prove that the locus of middle points of chords of constant length 2d unit of the hyperbola `xy=c^(2)` is `(x^(2)+y^(2))(xy-c^(2))=d^(2)xy`.

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Prove that the locus of the mid-points of chords of length 2d unit of the hyperbola xy=c^(2) is (x^(2)+y^(2))(xy-c^(2))=d^(2)xy.

Prove that the locus of the mid-points of chords of length 2d units of the hyperbola xy=c^2 is (x^2+y^2)(xy-c^2)=d^2xy

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

x^(2)dy+(x^(2)-xy+y^(2))dx=0

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^(2)-y^(2)=a^(2)" is " a^(2)(y^(2)-x^(2))=4x^(2)y^(2) .

Prove that the locus of the point of intersection of the tangents at the ends of the normal chords of the hyperbola x^2-y^2=a^2 is a^2(y^2-x^2)=4x^2y^2dot

(x^(2)+xy)(dy)/(dx)=x^(2)+y^(2)

Prove that the area of the triangle formed by any tangent to the hyperbola xy=c^(2) and the coordinate axes is constant.

(x^(2)-2xy)dy+(x^(2)-3xy+2y^(2))dx=0

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

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  2. Vertices A(1,1) , B(4,-2) and (5,5) of a triangle are given , find the...

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  3. Prove that the locus of middle points of chords of constant length 2d ...

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  4. Find the integer values of m for which x-coordinate of the point of in...

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  5. A chord AB of the circle x^(2)+y^(2)=a^(2) subtends a right angle at i...

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  6. The corodinates of the three vertices of a triangle are (a, a tan alph...

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  7. The triangle PQR is inscribed in the circle x^(2)+y^(2)=25. If Q and ...

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  8. Let L(1) be a striaght line passing through the origin and L(2) be the...

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  9. A rectangle PQRS has its side PQ paralle to the line y=mx and vertices...

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  10. If two distinct chords, drawn from the point (p,q) on the circle x^(2)...

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  11. A variable line L passing through the point B(2,5) intesects the lines...

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  12. For all values of a and, b show that the circle (x-2)(x-2+a)+(y+3) (y+...

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  13. A circle C(1) of diameter 6 units, is in the first quadrant and it tou...

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  14. Find he point on the straight line y=2x+11 which is nearest to the cir...

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  15. On the parabola y^(2)=4ax, P is the point with parameter t,Q is the op...

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  16. Through the vertex A of a parabola the chords AP and AQ are drawn at ...

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  17. Show that the sum of the ordinate of end of any chord of a system of p...

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  18. An equilateral triangle is inscribed within the parabola y^(2)=4ax wit...

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  19. P,Q and R three points on the parabola y^(2)=4ax. If Pq passes through...

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  20. A line of length (a+b) unit moves in such a way that its ends are alwa...

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