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If the circles x^2 + y^2 + 2ax + cy + a ...

If the circles `x^2 + y^2 + 2ax + cy + a =0` and `x^2 + y^2 - 3ax + dy - 1 = 0` intersect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for

A

exactly one value of 'a'

B

no value of 'a'

C

infinitely many values of 'a'

D

exactly two values of 'a'

Text Solution

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The correct Answer is:
B
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AAKASH SERIES-SYSTEM OF CIRCLES-Exercise-II (Class work)
  1. The centres of the circles are (a, c) and (b, c) and their radical axi...

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  2. (a,0) and (b, 0) are centres of two circles belonging to a co-axial sy...

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  3. If the circles x^2 + y^2 + 2ax + cy + a =0 and x^2 + y^2 - 3ax + dy - ...

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  4. The radical centre of the circles x^2+y^2-x+3y-3=0 , x^2+y^2-2x+2y-2=0...

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  5. The centre of the circle orthogonal to the circles x^2+y^2+4y+1=0 , x^...

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  6. The point from which the tangents to the circles x^2+y^2-8x+40=0, 5x^2...

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  7. You are given n ( ge 3) circles having different radical axes and rad...

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  8. If A, B, C are the centres of three circles touching mutually external...

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  9. The radical centre of the three circles described on the three sides o...

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  10. ABC is a triangle. The radical centre of the circles with AB, BC, CA a...

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  11. A, B, C are the centres of three circles of equal radii which donot to...

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  12. A,B,C are the centres of the three circles C1,C2,C3 such that C1,C2 ...

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  13. The slope of the radical axis of the circles x^2+y^2+3x+4y-5=0 and x^2...

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  14. The distance of the point (1,-2) from the common chord of the circles ...

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  15. The length of the common chord of the circles x^(2) + y^(2) + 2x + ...

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  16. The length of the common chord of the circles (x-6)^2+(y-4)^2=4, (x-4)...

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  17. If the circle x^(2) +y^(2) + 2gx + 2fy + c = 0 bisects the circumfer...

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  18. The condition that the circle x^(2) +y^(2) + 2gx+ 2fy + c = 0 to bisec...

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  19. The length of the common chord of the two circles (x-a)^2+(y-b)^2=c^2,...

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  20. The circle on the chord xcos alpha + ysin alpha =p of the circle x^2+y...

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