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If x cos alpha+ y sin alpha=p, where p=(...

If `x cos alpha+ y sin alpha=p`, where `p=(-sin^(2) alpha)/(cos alpha)` be a straight, line, prove that the perpendicular `p_(1), p_(2) and p_(3)` on this line drawn from the point `(m^(2), 2m), (mm', m+m' and) ((m')^(2), 2m')` respectively, are in geometric progression. `(m gt 0, m gt 0, 0 lt alpha lt 90^(@))`.

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. The circle A and B of a line segment of constant length c unit slides ...

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  2. A variable striaght line of slope 4 intresects the hyprbola xy=1 at tw...

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  3. If x cos alpha+ y sin alpha=p, where p=(-sin^(2) alpha)/(cos alpha) be...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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