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If the distances from the origin to the centres of the three circles `x^2+ y^2-2 lamda x= c^2`, where c is constant and `lamda` is variable, are in G.P., prove that the lengths of tangents drawn from any point on the circle `x^2 +y^2= c^2` to the three circles are also in GP.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
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  2. If lines 5x + 12y-10 = 0 and 5x- 12y - 40 =0 touch a circle C1 of diam...

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Find the slope of the line passing through the points : (3, - 2) and...

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  16. The slope of the line passing through the points (3,-2) and (-1,4) is:

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  17. Slope of the line passing through the points (3, -2) and (3, 4) is:

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  18. If the equation of a circle is: x^2 + y^2 + 8x -10y+8=0, then its cent...

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  19. The centre of the circle x^(2)+y^(2)-6x+4y-1=0 is

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  20. If the equation of a circle is: x^2 + y^2-4x-8y -45 =0, then its centr...

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