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A variable circle passes through the poi...

A variable circle passes through the point `P (1, 2)` and touches the x-axis. Show that the locus of the other end of the diameter through `P` is `(x-1)^2 = 8y`.

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A DAS GUPTA-Circles-EXERCISE
  1. A point moves such that the sum of the squares of its distances from t...

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  2. Two rods of lengths aa n db slide along the x- and y-a xi s , respecti...

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  3. A variable circle passes through the point P (1, 2) and touches the x-...

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  4. From the point A (0, 3) on the circle x^2+4x+(y-3)^2=0 a chord AB is d...

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  5. From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1. The...

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  6. A circle of radius 'r' passes through the origin O and cuts the axes a...

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  7. A circle of radius r passes through the origin O and cuts the axes at ...

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  8. Find the locus of the midpoint of the chords of the circle x^2+y^2=a^2...

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  9. Let A be one point of intersection of two intersecting circles with ce...

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  10. Prove that the locus of a point which moves such that the sum of th...

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  11. The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes i...

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  12. A triangle has two of its sides along the axes, its third side touches...

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  13. The locus of the perpendiculars drawn from the point (a, 0) on tange...

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  14. Let S-=x^2+y^2+2gx+2f y+c= be a given circle. Find the locus of the fo...

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  15. Show that the locus of points from which the tangents drawn to a circl...

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  16. Find the locus of the point of intersection of tangents to the circle ...

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  17. The circle x^2+y^2-4x-4y+4=0 is inscribed in a triangle which has two ...

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  18. The locus of the centres of the circles which touch x^2+y^2=a^2 and x^...

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  19. Locus of the point of intersection of perpendicular tangents to the ...

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  20. If the polar of a point (p,q) with respect to the circle x^2 +y^2=a^2 ...

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