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The line 2x - 3y +1=0 is tangent to a ...

The line `2x - 3y +1=0` is tangent to a circle S=0 at `(1, 1)`. If the radius of the circle is `sqrt13`. Find theequation of the circle S.

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The correct Answer is:
`x^(2) + y^(2) - 6x + 4y = 0` or `x^(2) + y^(2) + 2x - 8y + 4 = 0`
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MOTION-CIRCLE-Exercise - 3 (Subjective | JEE Advanced)
  1. Find the locus of the middle points of portions of the tangents to the...

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  2. Find the equation of the circle passing through the three points (4, 7...

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  3. The line 2x - 3y +1=0 is tangent to a circle S=0 at (1, 1). If the r...

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  4. A circle with center in the first quadrant is tangent to y = x+10, y =...

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  5. A circle C is tangent to the x and y axis in the first quadrant at the...

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  6. Tangents are drawn to the concentric circles x^2+y^2=a^2 and x^2 +y^2=...

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  7. Find the locus of the mid point of the chord of a circle x^(2) + y^(2)...

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  8. Find the equation of circle passing through (1, 1) belonging to the sy...

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  9. A circle S = 0 is drawn with its centre at (-1, 1) so as to touch the ...

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  10. Find the equation of the circle which passes through the point (1, 1) ...

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  11. Find the equation of the circle whose radius is 3 and which touches ...

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  12. Find the equation of the circle whose diameter is the common chord of ...

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  13. If the radical axis of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3...

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  14. Find the equation of the circle through the points of intersection of ...

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  15. The centre of the circle S=0 lie on the line 2x – 2y +9=0 & S=0 cuts o...

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  16. Find the equation of a circle passing through the origin if the line p...

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  17. Find the equation of the circle which cuts the circle x^2 + y^2 - 14x...

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  18. The locus of the centers of the circles which cut the circles x^(2) + ...

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  19. The equation of a circle which touches the line x +y= 5 at N(-2,7) and...

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  20. Find the equation of the circle passing through the point (– 6, 0) if ...

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