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Prove that the centres of the three circ...

Prove that the centres of the three circles : `x^2 + y^2 -4x-6y-14=0, x^2 + y^2+ 2x+4y-5=0` and `x^2 + y^2-10x -16y + 7 = 0` are collinear.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Let (2, 1), (- 3, -2) and (a, b) form a triangle. Show that the collec...

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  2. Does the point (-2.5, 3.5) lie inside, outside or on the circle x^2 + ...

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  3. Prove that the centres of the three circles : x^2 + y^2 -4x-6y-14=0, x...

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  4. Prove that, through three given points which are not collinear, there ...

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  5. Find equations to the circles touching Y-axis at (0,3) and making inte...

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  6. Find the area of the equilateral triangle that can be inscribed in the...

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  7. Find the equation of the circle circumscribing the quadrilateral forme...

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  8. If lines 5x + 12y-10 = 0 and 5x- 12y - 40 =0 touch a circle C1 of diam...

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  9. If the distances from the origin to the centres of the three circles x...

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  10. Determine the equation of the circle whose diameter is the chord x + y...

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  11. A rectangle ABCD is inscribed in a circle with a diameter lying along ...

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  12. Find the equation of the circle, which passes through the origin and c...

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  13. Prove that the equation y^2+ 2Ax + 2By +c =0 represents a parabola who...

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  14. A double ordinate of the parabola y^2=4ax is of length 8a. Prove that ...

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  15. Prove that the equation of the parabola whose vertex and focus are on ...

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  16. Find the focus of the parabola x^2=4y

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  17. Show that the locus of the middle points of normal chords of the parab...

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  18. If any tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cuts off inter...

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  19. The vertices of a quadrilateral are situated at foci and the extremiti...

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  20. Find the equation of the hyperbola whose foci are (8, 3), (0, 3) and w...

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