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Prove that the two circles x^2+y^2+2by+c...

Prove that the two circles `x^2+y^2+2by+c^2=0` and `x^2+y^2+2ax+c^2=0`, will touch each other `1/a^2+1/b^2=1/c^2`.

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Prove that the circles given by x^2+y^2+2ax+2by+c=0 , and x^2+y^2+2bx+2ay+c=0 , touch each other, if (a + b)^2 = 2c.

Prove that the circles given by the equations x^2+y^2+2x-8y+8=0 and x^2+y^2+10x-2y+22=0 touches each other externally. Find also the point of contact.

Prove that the circles given by the equations x^2+y^2=4 and x^2+y^2+6x+8y-24=0 touche each other and find the equation of the common tangent.

Find the equation of the circle passing through the intersection of the circles, x^2+y^2-2ax=0 and x^2+y^2-2by=0 and having the centre on the line x/a - y/b = 2.

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MBD PUBLICATION-CONIC SECTIONS-QUESTION BANK
  1. Prove that the circles given by the equations x^2+y^2+2x-8y+8=0 and x^...

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  2. Prove that the circles given by the equations x^2+y^2=4 and x^2+y^2+6x...

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  3. Prove that the two circles x^2+y^2+2by+c^2=0 and x^2+y^2+2ax+c^2=0, wi...

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  4. Prove that the circles given by x^2+y^2+2ax+2by+c=0, and x^2+y^2+2bx+2...

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  5. Find the equation of the circle through the point of intersection of c...

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  6. Find the equation of the circle passing through the intersection of th...

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  7. Find the radical axis of the circles x^2+y^2-6x-8y-3=0 and 2x^2+2y^2+4...

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  8. Find the radical axis of the circles x^2+y^2-6x+8y-12=0 and x^2+y^2+6x...

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  9. If centre of one circle lies on or inside another, prove that the circ...

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  10. If a circle S intersects circles S1 and S2 orthogonally. Prove that th...

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  11. R is the radical centre of circles S1, S2 and S3. Prove that if R is o...

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  12. Determine a circle which cuts orthogonally each of the circles. S1 : x...

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  13. Prove that on pair of concentric circles can have a radical axis.

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  14. The equation of the directrix to the parabola x^2=-6yis .

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  15. The eccentricity of the parabola y^2=8xis .

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  16. The line y+x=k is tangent to the parabola y^2+12x=0 if k=.

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  17. The latus rectum of the parabola (y-2)^2=8(x+3) is .

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  18. The equation of tangent to the parabola x^2=6y at vertex is .

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  19. The equation of axis of the ellipse x^2/16+y^2/9=1 is .

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  20. The equation of the major axis of ellipse (x+1)^2/16+(y-2)^2/9=1 is .

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