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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

A

imaginary

B

real and equal

C

real and unequal

D

rational

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-CIRCLES-Exercise
  1. The tangent at P, any point on the circle x^2 +y^2 =4 , meets the coor...

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  2. The equation of the circle which touches the axes of coordinates and ...

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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 from the origin a chord is drawn to the circle x^(2)+y^(2)-2x=0, t...

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  5. The locus represented by x=a/2(t+1/t), y=a/2(t-1/t) is

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

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  7. Find the locus of the midpoint of the chord of the circle x^2+y^2-2x-2...

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  8. The two circles x^(2)+y^(2)-2x-3=0 and x^(2)+y^(2)-4x-6y-8=0 are such ...

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  9. The equation of the circle having its centre on the line x+2y-3=0 and ...

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  10. The equation of the circumcircle of the triangle formed by the lines y...

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  11. The equation x^(2)+y^(2)+4x+6y+13=0 represents

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  12. To which of the circles, the line y-x+3=0 is normal at the point (3+3s...

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  13. Circles are drawn through the point (2, 0) to cut intercept of length ...

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  14. Find the equation of the circle which touches both the axes and the ...

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  15. The slope of the tangent at the point (h, h) of the circle x^(2)+y^(2...

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  16. The two circles x^2+ y^2=r^2 and x^2+y^2-10x +16=0 intersect at two d...

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  17. Locus of thews of the centre of the circle which touches x^2+y^2 - 6x-...

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  18. If a circle passes through the point (a, b) and cuts the circlex x^2+y...

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  19. The locus of the mid-point of the chords of the circle x^2+y^2=4 wh...

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  20. Two circle x^2+y^2=6 and x^2+y^2-6x+8=0 are given. Then the equation o...

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