Q. 34.0( 8 Votes )

# Find the eq

Answer :

Given that we need to find the equation of the circle which passes through (3, - 2), (- 2,0) and has its centre on the line 2x - y = 3. ..... (1) We know that the standard form of the equation of the circle is given by:

x2 + y2 + 2ax + 2by + c = 0 .....(2)

Substituting centre (- a, - b) in (1) we get,

2(- a) - (- b) = 3

- 2a + b = 3

2a - b + 3 = 0 ......(3)

Substituting (3, - 2) in (2), we get

32 + (- 2)2 + 2a(3) + 2b(- 2) + c = 0

9 + 4 + 6a - 4b + c = 0

6a - 4b + c + 13 = 0 ..... (4)

Substituting (- 2,0) in (2), we get

(- 2)2 + 02 + 2a(- 2) + 2b(0) + c = 0

4 + 0 - 4a + c = 0

4a - c - 4 = 0 ..... (5)

Solving (3), (4) and (5) we get, Substituting these values in (2), we get x2 + y2 + 3x + 12y + 2 = 0

The equation of the circle is x2 + y2 + 3x + 12y + 2 = 0.

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