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Prove that the centres of the circles `x^2+y^2=1`, `x^2+y^2+6x-2y-1=0` and `x^2+y^2-12x+4y=1` are collinear

A

a)vertices of an equilateral `/_\`

B

b)vertices of a right-angles traingle

C

c)collineat

D

d)none of these

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Prove that the radii of the circles x^(2)+y^(2)=1,x^(2)+y^(2)-2x-6y=6and x^(2)+y^(2)-4x-12y-9=0 are in arithmetic progression.

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A DAS GUPTA-Circles-EXERCISE
  1. For any lambda in R, the locus x² + y² - 2lambdax - 2lambday +lambda²=...

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  2. Find the equation of the circle which touch the line 2x-y=1 at (1,1) a...

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  3. The circle for which the points (am^2,2am) and (a/m^2, (-2a)/m) are th...

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  4. The radius of the circle passing through the point (6,2) and having x ...

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  5. A circle passes through point (3, sqrt(7/2)) and touches the line-pai...

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  6. The angle between a pair of tangents from a point P to the circe x^2 +...

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  7. Let AB be a line segment of length 4 with A on the line y = 2x and B o...

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  8. The locus of the centre of a circle which touches externally the circl...

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  9. Prove that the centres of the circles x^2+y^2=1, x^2+y^2+6x-2y-1=0 and...

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  10. Find the equation of the circle which passes through the origin and...

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  11. The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

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  12. The lines 2x+3y+19=0 and 9x+6y-17=0 , cut the coordinate axes at concy...

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  13. The area of an equilateral triangle inscribed in the circle x^2 + y^2-...

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  14. The range of values of a such that the angle theta between the pair of...

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  15. Let A-=(-1,0),B-=(3,0), and P Q be any line passing through (4, 1) hav...

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  16. (C) 2 45. Three concentric circles of which the biggest is x^2+ y^2= 1...

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  17. The equation of radical axis of two circles is x + y = 1. One of the ...

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  18. Find the locus of the centers of the circles x^2+y^2-2x-2b y+2=0 , whe...

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  19. The range of parameter ' a ' for which the variable line y=2x+a lies b...

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  20. Let C1and C2 be two circles with C2 lying inside C1 circle C lying ins...

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