The equation of the circumcircle of the triangle formed by the lines x-0- y-0-2 x-3 y-5 is A- 6 x 2- y 2-53 x -2 y -0B- x 2- y 2-2 x -3 y -5-0C- x2-y2-2 x-3 y-5-0D- 6x2-y2-53 x-2 y-0

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Circle Inscribing a Triangle Formed by 3 Given Lines

The equation ...

Question

The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is

x^{2} + y^{2} + 2 x + 3 y - 5 = 0

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6 (x^{2} + y^{2}) - 5 (3 x + 2 y) = 0

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x^{2} + y^{2} - 2 x - 3 y + 5 = 0

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6 (x^{2} + y^{2}) + 5 (3 x + 2 y) = 0

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Solution

The correct option is B $6 (x^{2} + y^{2}) - 5 (3 x + 2 y) = 0$
Given, triangle formed by the lines x = 0, y = 0, 2x + 3y = 5, so vertices of the triangle are (0, 0), (5/2, 0) and (0, 5/3).
Since circle is passing through (0, 0).

$∴$ Equation of circle will be $x^{2} + y^{2} + 2 g x + 2 f y = 0$ ...(i)

Also, circle is passing through (5/2, 0) and (0, 5/3)
So, g = -5/4, f = -5/6.
Put the values of g and f in equation (i).
After solving, we get $6 (x^{2} + y^{2}) - 5 (3 x + 2 y) = 0,$ which is the required equation of the circle.

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