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P is any point on the x-a=0. If A=(a,0)a...

P is any point on the `x-a=0`. If `A=(a,0)`and PQ , the bisector of `angleOCA` meets the x-axis in Q prove that the locus of the foot of prependicular from Q on Op is `(x-a)^2(x^2+y^2)=a^2y^2`

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A DAS GUPTA-Coordinates and Straight Lines-EXERCISE
  1. If P(1,0), Q(-1,0) and R (2,0) are three given points, then the locus ...

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  2. If the sum of the distances of a point from two perpendicular lines in...

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  3. The image of the point (-1,3) by the line x - y = 0 , is

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  4. The point (4, 1) undergoes the following three transformations success...

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  5. All points lying inside the triangle formed by the points (1,3) ,(5,0)...

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  6. The two line segment joining (-2,7), (-5,-3) and (-8,-13),(1,17) cut e...

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  7. If line y - x + 2 = 0 is shifted parallel to itself towards the x-axis...

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  8. If the point (a^2,a+1) lies in the angle between the lines 3x-y+1=0 an...

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  9. The locus of a point which moves so that the difference of the squares...

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  10. If |x1y1 1x2y2 1x3y3 1|=|a1b1 1a2b2 1a3b3 1| then the two triangles ...

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  11. The straight line passing through the point of intersection of the str...

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  12. State whether the statements are true or false. The perpendicular bise...

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  13. P(m, n) (where m, n are natural numbers) is any point in the interior ...

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  14. If alpha,alpha^2) falls inside the angle made by the lines 2y=x ,x >0&...

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  15. The image of the point A (1,2) by the line mirror y=x is the point B a...

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  16. A=(sqrt(1-t^2)+t, 0) and B=(sqrt(1-t^2)-t, 2t) are two variable points...

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  17. If one diagonal of a square is the portion of the line x/a + y/b = 1 ...

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  18. The three intercepts made on the line x+y=5sqrt(2) by the lines y=x ta...

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  19. Let the coordinates of the foot of the perpendicular from the vertices...

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  20. P is any point on the x-a=0. If A=(a,0)and PQ , the bisector of angleO...

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