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Q57) If the circle x^2+y^2+2ax+cy+a=0 an...

Q57) If the circle `x^2+y^2+2ax+cy+a=0 and x^2+y^2-3ax+dy-1=0 `intersect at two distinct points Pand Q, then the line 5x+by-a=0 will pass through P and Q for A. No values of a B. Exactly one value of a C. Exactly two values of a D. Infinitely many value of a

A

inifinitely many vlaues of a

B

exctly two values of a

C

Exactly one value of a

D

no value of a

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The correct Answer is:
D
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MCGROW HILL PUBLICATION-CIRCLES AND SYSTEMS OF CIRCLES -QUESTIONS FROM PREVIOUS YEARS. AIEEE/JEE MAIN PAPERS
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  3. Q57) If the circle x^2+y^2+2ax+cy+a=0 and x^2+y^2-3ax+dy-1=0 intersect...

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

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  5. A circle touches the x-axis and also touches the circle with center (...

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  6. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

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  7. If the lines 3x-4y-7 = 0 and 2x-3y-5=0 are two diameters of a circle o...

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  8. Consider a family of circles which are passing through the point (-...

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  9. The point diametrically opposite to the point P(1, 0) on the circle x^...

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  10. Three distinct points A, B and C are given in the 2–dimensional coor...

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  11. If P and Q are the points of intersection of the circles x^2+""y^2+...

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  12. If the two circles x^(2) + y^(2) + ax = 0 " and " x^(2) + y^(2) = c^(...

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  13. The equation of the circle passing through the point (1,0) and (0,1) a...

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  14. The two circles x^(2)+y^(2)=ax and x^(2)+y^(2)=c^(2)(c gt 0) touch eac...

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  15. The length of the diameter of the circle which touches the x-axis at t...

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  16. The circle passing through (1, -2) and touching the axis of x at (3...

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  17. If each of the lines 5x + 8y = 13 and 4x - y = 3 contains a diameter o...

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  18. lf a circle C passing through (4,0) touches the circle x^2 + y^2 + 4x-...

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  19. If two vertices of an equilateral triangle are A (-a,0)and B (a,0), a ...

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  20. If the circle x ^(2) +y ^(2) - 6x - 8y + (25 -a ^(2)) =0 touches the a...

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