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If the chord of contact of the tangents from a point on the circle `x^2 + y^2 = a^2` to the circle `x^2 + y^2 = b^2` touch the circle `x^2 +y^2 = c^2`, then the roots of the equation `ax^2 + 2bx + c = 0` are necessarily. (A) imaginary (B) real and equal (C) real and unequal (D) rational

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A DAS GUPTA-Circles-EXERCISE
  1. A straight line AB is divided at C so that AC=3CB. Circles are describ...

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  2. If from any point P on the circle x^2+y^2+2gx+2fy+c=0 tangents are dra...

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  3. If the chord of contact of the tangents from a point on the circle x^2...

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  4. If the pole of a straight line with respect to the circle x^(2)+y^(2)=...

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  5. Tangents are drawn from the point (h,k) to ^circle x^2+y^2 =a^2; Prove...

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  6. Find the equation of the circle which has for its diameter the chord o...

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  7. If y=mx be the equation of a chord of the circle prove that the circle...

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  8. Prove that the circle x^2 + y^2-6x-4y+9=0 bisects the circumference of...

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  9. The equation of the circle on the common chord of the circles (x-a)^(2...

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  10. Find the equation of the circle passing through the intersection of th...

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  11. Find the equation of the circle passing through the point of intersect...

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  12. Find the equation of the circle whose diameter is the common chord of ...

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  13. The line Ax+By+=0 cuts the circle by x^2+y^2+Ax+By+C=0at P and Q. The ...

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  14. Prove that the equation x^(2)+y^(2)-2x-2ay-8=0, a in R represents the...

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  15. The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing ...

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  16. Consider a family of circles passing through two fixed points A (3,7) ...

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  17. If the circle C1: x^2 + y^2 = 16 intersects another circle C2 of radiu...

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  18. The equation of the circle passing through the origin & cutting the ci...

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

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

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