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From the point A (0,3) on the circle x...

From the point A `(0,3)` on the circle
`x^(2)+ 4x+(y-3)^(2) = 0` a chord AB is drawn
and extended to a point M such that
AM = 2 AB. Find the equation of the locus
of M.

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Verified by Experts

The correct Answer is:
` therefore ` Locus of M is ` x^(2) + y ^(2) + 8x- 6y + 9=0 `, which is a circle.
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AAKASH SERIES-CIRCLE-EXERCISE -1.4
  1. From the point A (0,3) on the circle x^(2)+ 4x+(y-3)^(2) = 0 a chord...

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  2. Discuss the relative position of the fol- lowing pair of circles. ...

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  3. Discuss the relative position of the fol- lowing pair of circles. ...

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  4. Find the number of possible common tangents that exist for the follo...

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  5. Find the number of possible common tangents that exist for the follo...

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  6. Find the number of possible common tangents that exist for the follo...

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  7. Show that the circles x^(2) +y^(2) -4x-6y-12=0 and 5(x^(2)+y^(2))-...

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  8. Show that x^(2) + y^(2) -6x -9y +13 =0, x^(2) +y^(2) -2x -16y =0 touch...

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  9. Show that the circles x^(2) + y^(2)-4x-6y-12=0 and x^(2) +y^(2) +...

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  10. Find the equation of the circle which touches the circle x^(2) + y^(...

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  11. Show that the circles S=-x^(2) + y^(2) -2x-4y -20 =0 , S' = x^(2) +y^...

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  12. Show that the four common tangents can be drawn for the circles give...

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  13. Prove that the circles x^(2) + y^(2) -8x -6y +21=0 and x^(2) + y^(2) ...

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  14. Find the direct common tangents of the circles x^(2) + y^(2) +22x -4y...

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  15. Find the transberes common tangents of the circles x^(2) + y^(2) -4...

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  16. Find all common tangents of the pairs of circles x^(2) +y^(2) =0 a...

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  17. Find all common tangents of the pairs of circles x^(2) +y^(2) +4x ...

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  18. Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0. Suppose that...

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  19. Find the value of c for which A(2,0),B(0,14//3) ,C(4,5) and D(0,c) a...

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  20. The area of the quadrilateral formed by the tangents from the point (4...

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  21. Discuss the relative position of the fol- lowing pair of circles. ...

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