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Find the pair of tangents form the origi...

Find the pair of tangents form the origin
to the circle `x^(2) + y^(2) + 2gx + 2fy + c = 0`
and hence deduce a condition for these
tangents to be perpendicular.

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Verified by Experts

The correct Answer is:
`( gx+fy)^(2) =c(x^(2) +y^(2) ) , g^(2) +f^(2) =2c`
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AAKASH SERIES-CIRCLE-EXERCISE -1.3
  1. Find the pair of tangents drawn from (3,2) to the circle x^(2) + y^...

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  2. Find the pair of tangents drawn from (1,3) to the circle x^(2) + y^...

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  3. Find the pair of tangents form the origin to the circle x^(2) + y^(2...

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  4. Find the chord of contact of (1,1 ) with respect to the circle x...

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  5. Find the chord of contact of (0,5) with respect to the circle x(...

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  6. Find the polar of (1,2) with respect to x^(2) + y^(2) = 7

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  7. Find the polar of (3, -1) with respect to 2x^(2) + 2y^(2) = 11

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  8. Find the polar of (1,-2) with respect of x^(2) + y^(2) - 10 x - 10y ...

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  9. Find the pole of 3x + 4y -0 45 = 0 with respect to x^(2) + y^(2) - ...

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  10. Find the pole of x-2y + 22 = 0 with respect to x^(2) + y^(2) - 5 x ...

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  11. Find the slope of the polar of (1, 3) with respect to the circle x^(...

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  12. If ax + by + c = 0 is the polar of (1,1) with respect to the circle x^...

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  13. Find the coordinates of the point of intersection of tangent at the po...

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  14. (prove that) If the polar of the points on the circle x^(2) + y ^(2)...

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  15. Tangents are drawn to the circle x^(2) + y^(2) = 16 from the point ...

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  16. Find the locus of the point whose polars with respect to the circles x...

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  17. The locus of poles of tangents to the circle (x-p)^(2)+y^(2)=b^(2) w.r...

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  18. If the polars of the points (x1,y1) ,(x2,y2) and (x3,y3) with respec...

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  19. Show that (-6,1) and (2,3) are conjugate points w.r.t. the circle...

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  20. Show that (-6,1) and (2,3) are conjugate points w.r.t. the circle...

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