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From a point P, tangents drawn to the ci...

From a point `P`, tangents drawn to the circle `x^2 + y^2 + x-3=0, 3x^2 + 3y^2 - 5x+3y=0 and 4x^2 + 4y^2 + 8x+7y+9=0` are of equal lengths. Find the equation of the circle through `P`, which touches the line `x+y=5` at the point `(6, -1)`.

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A DAS GUPTA-Circles-EXERCISE
  1. Find the equation of a circle which is co-axial with circles 2x^2 + 2y...

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  2. The equation of three circles are given x^2+y^2=1,x^2+y^2-8x+15=0,x^2+...

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  3. From a point P, tangents drawn to the circle x^2 + y^2 + x-3=0, 3x^2 +...

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  4. Let A = (-2,0) and B = (1,0) and P is a variable point such that /APB ...

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  5. A point moves such that the sum of the squares of its distances from t...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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