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If a circle S intersects circles S1 and ...

If a circle S intersects circles `S_1` and `S_2` orthogonally. Prove that the centre of S lies on the radical axis of `S_1` and `S_2`.

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MBD PUBLICATION-CONIC SECTIONS-QUESTION BANK
  1. 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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  2. If centre of one circle lies on or inside another, prove that the circ...

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

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

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

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

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

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

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

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

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

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

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

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  14. The distance between the focii of the ellipse 3x^2+4y^2=1 is .

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  15. The ecentricity of the ellipse x^2/16+y^2/25=1 is .

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  16. The line y=2x+k is a tangent to the ellipse 5x^2+y^2=5 if k =.

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  17. The length of the latus rectum of the ellipse (x-2)^2/4+(y+3)^2/25=1 i...

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  18. The equation of the conjugate axis of the hyperbola x^2/9-(y+2)^2/16=1...

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  19. The hyperbola y^2/16-x^2/12=1 intersects x-axis at .

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  20. The eccentricity of the parabola 4x^2-3y^2=1 is .

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