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A(x(1) y(1)) and B(x(2), y(2)) are two g...

`A(x_(1) y_(1)) and B(x_(2), y_(2))` are two given points on a circle. If the chord AB substends an angle `theta` at a point p on its circumferene, show that the equation of the circle is
`(x-x_(1)) (x-x_(2))+(y-y_(1))(y-y_(2))=+- cos theta [ (x-x_(1))(y-y_(2))-(x-x_(2))(y-y_(1))]`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. If x cos alpha+ y sin alpha=p, where p=(-sin^(2) alpha)/(cos alpha) be...

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  2. A tangent drawn from the point (4,0) to the circle x^(2)+y^(2)=8 touch...

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  3. A(x(1) y(1)) and B(x(2), y(2)) are two given points on a circle. If th...

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  4. If 4a^(2)-5b^(2)+6a+1=0 find the equation of the circle for which the...

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  5. Find the point of the circle x^(2)+y^(2)-6x+4y=0 which is (i) nearest ...

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  6. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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