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The equation of circle passing through `(1,-3)` and the points common to the two circt `x^2 + y^2 - 6x + 8y - 16 = 0, x^2 + y^2 + 4x - 2y - 8 = 0` is

A

`x^(2)+y^(2)-4x+6y+24=0`

B

`2x^(2)+2y^(2)+3x+y-20=0`

C

`3x^(2)+3y^(2)-5x+7y-19=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
The required circle is
`(x^(2)+y^(2)-6x+8y-16)+lambda(x^(2)+y^(2)+4x-2y-8)=0` [Using: `S_(1)+lambda S_(2)=0`]
This passes through (1, -3).
`:. (1+9-6-24-16)+lambda(1+9+4+6-8)=0`
`rArr -36+lambda(12)=0 rArr lambda=3`
So, the equation of the required circle is
`4x^(2)+4y^(2)+6x+2y-40=0`
`rArr 2x^(2)+2y^(2)+3x+y-20=0`
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OBJECTIVE RD SHARMA-CIRCLES-Chapter Test
  1. The equation of circle passing through (1,-3) and the points common to...

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  2. The two circles x^2 + y^2 -2x+6y+6=0 and x^2 + y^2 - 5x + 6y + 15 = 0 ...

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  3. The two circles x^(2)+y^(2)-2x-2y-7=0 and 3(x^(2)+y^(2))-8x+29y=0

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  4. The centre of the circle passing through (0, 0) and (1, 0) and touchin...

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  5. The circle x^2+y^2=4 cuts the circle x^2+y^2+2x+3y-5=0 in A and B, The...

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  6. One of the limit point of the coaxial system of circles containing x^(...

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  7. A circle touches y-axis at (0, 2) and has an intercept of 4 units on t...

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  8. The equation of the circle whose one diameter is PQ, where the ordinat...

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  9. The circle x^2 + y^2+ 4x-7y + 12 = 0 cuts an intercept on y-axis equal...

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  10. Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0...

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  11. The angle between the pair of tangents from the point (1, 1/2) to the...

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  12. The intercept on line y = x by circle x^2 + y^2- 2x = 0 is AB. Find eq...

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  13. If 3x+y=0 is a tangent to a circle whose center is (2,-1) , then find ...

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  14. Locus of the middle points of chords of the circle x^2 + y^2 = 16 whic...

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  15. Two tangents to the circle x^2 +y^2=4 at the points A and B meet at P(...

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  16. A tangent is drawn to the circle 2(x^(2)+y^(2))-3x+4y=0 and it touch...

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  17. the length of the chord of the circle x^(2)+y^(2)=25 passing through ...

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  18. If the points A(2, 5) and B are symmetrical about the tangent to the c...

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  19. The equation of the circle of radius 2sqrt(2) whose centre lies on the...

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  20. Prove that the maximum number of points with rational coordinates on a...

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  21. The equation of a circle C is x^(2)+y^(2)-6x-8y-11=0. The number of re...

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