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Radii of circles x^(2) + y^(2) = 1, x^(...

Radii of circles ` x^(2) + y^(2) = 1, x^(2) + y^(2) - 2x - 6y= 6` and
` x^(2) + y^(2) - 4x - 12y = 9 ` are in

A

A .P

B

G.P.

C

H.P.

D

no progression

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The correct Answer is:
D
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If r_(1), r_(2) " and " r_(3) are the radii of the circle x^(2) + y^(2) - 4x + 6y = 5 , x^(2) + y^(2) + 6x - 4y = 3 " and " x^(2) + y^(2) - 2x + 4y = 8

2.10 The radii of the circles x2 + y2 = 1, x2 + y2 – 2x – 6y = 6 and x2 + y2 - 4x - 12y = 9 are in(A)AP.(B)GP.(C) H.P.(D) None

The centres of the circles x ^(2) + y ^(2) =1, x ^(2) + y^(2)+ 6x - 2y =1 and x ^(2) + y^(2) -12 x + 4y =1 are

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.

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

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

The circles x^(2)+y^(2)+6x+6y=0 and x^(2)+y^(2)-12x-12y=0

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

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

MARVEL PUBLICATION-CIRCLE AND CONICS -MULTIPLE CHOICE QUESTIONS
  1. Equations of diameters of circle (x-5)(x-1) + (y - 7) (y-1) = 0 ....

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  2. If circle x (x -1) + y (y -1) = c(x + y -1) touches X-axis , then c...

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  3. Radii of circles x^(2) + y^(2) = 1, x^(2) + y^(2) - 2x - 6y= 6 and ...

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  4. A circle of radius 2 lies in the first quadrant and touches both the a...

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  5. Find the equation of the circle the end points of whose diameter are t...

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  6. The sides of a square are x=2,x=3,y=1andy=2. Find the equation of the ...

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  7. If (2,-1) lies on x^(2) + y^(2) + 2gx + 2fy + c = 0 , which is conc...

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  8. If one end of a diameter of the circle x^2 + y^2 - 8x - 14y+c=0 is the...

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  9. If ends of a diameter of a circle are (-4,3) and (12,-1) , then y-i...

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  10. If abscissas and ordinates of points A , B are roots of equation ...

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  11. Equation of that diameter of circle x^(2) + y^(2) - 6x + 2y - 8 = 0 ...

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  12. Equation of circle , concentric with circle x^(2) + y^(2) - 6x + 12...

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  13. Equation of circle which touches line x = y at the origin , and passe...

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  14. If equation of a circle is (4a - 3) x^(2) +ay^(2) + 6x - 2y + 2 = 0 ,...

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  15. If the equation 3x^(2) + 3y^(2) + kxy + 9x + (k - 6) y + 3 = 0 rep...

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  16. Equation x^(2) + y^(2) - 8x + 6y + 25 = 0 represents

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  17. If lines 12 x + 5y + 16 = 0 " and " 12 x + 5y - 10 = 0 both touch ...

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  18. Abscissas and ordinates of points A and B are roots of equation x^(...

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  19. Two points on the circle x^(2) + y^(2) - 12x - 16y + 75 = 0 , one ...

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  20. Two circles x^(2) + y^(2) - 2x - 4y = 0 and x^(2) + y^(2) - 8y...

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