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Find the radical axis of the circles x^2...

Find the radical axis of the circles `x^2+y^2-6x+8y-12=0` and `x^2+y^2+6x-8y+12=0`. Prove that the radical axis is perpendicular to the line joining the centers of the two circles.

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

Find the centre and radius of the following circles : x^2 + y^2 + 6x -4y -12 = 0

Find the centre and radius of the following circles : 4x^2 + 4y^2 - 4x + 12y - 15 = 0

Find the equation of the tangents to the circle x^2+y^2+4x-6y-16=0 at the point where it meets the y-axis.

Find the coordinates of the points where the circle x^2 + y^2 -7x - 8y + 12 = 0 meets the coordinates axes and hence find the intercepts on the axes.

Calculate the radii and distance between the centres of the circle whose equations are, x^2+y^2-16x-10y+8=0 x^2+y^2+6x-4y-36=0 Hence or otherwise prove that the tangents drawn to the circles at their points of intersection are perpendicular.

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.

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.

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MBD PUBLICATION-CONIC SECTIONS-QUESTION BANK
  1. Find the equation of the circle passing through the intersection of th...

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  2. 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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  3. 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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  4. If centre of one circle lies on or inside another, prove that the circ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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