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Prove that the two circles each of which...

Prove that the two circles each of which passes through the point `(0, k) and (0, -k)` and thouches the line `y=mx+b` will cut orthogonally, if `b^2 = k^2 (2+m^2)`.

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A DAS GUPTA-Circles-EXERCISE
  1. The equation of the circle passing through the origin & cutting the ci...

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  2. The equation of the circle which passes through the origin, center lie...

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  3. Prove that the two circles each of which passes through the point (0, ...

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  4. If the equations of two circles, whose radii are r and R respectively,...

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  5. The centre of the circle S=0 lies on the line 2x-2y+9=0 and it cuts th...

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  6. The centre of the circle that cuts the circle x^2 +y^2 + 2g x + 2fy + ...

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  7. Find the equation of a circle which is co-axial with circles 2x^2 + 2y...

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

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

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

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

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

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

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

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

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

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

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

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