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Length of Common Chord

Find the equa...

Question

Find the equation of the circle drawn on the intercept made by the line $2 x + 3 y = 6$ between the coordinate axes as diameter.

A

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

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B

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

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C

x^{2} - y^{2} - 2 x - y = 0

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D

None of these

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Solution

The correct option is C $x^{2} + y^{2} - 3 x - 2 y = 0$
The line $2 x + 3 y = 6$ meets $x$ and y-axes at $A (3, 0)$ and $B (0, 2)$ respectively. Taking AB as a diameter, the equation of the required circle is
$(x - 3) (x - 0) + (y - 0) (y - 2) = 0$
$x^{2} + y^{2} - 3 x - 2 y = 0$

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