Q. Equation of a circle passing through the origin and making intercept by the line $4x + 3y = 12$ with coordinate axes, is
A) $x^{2} + y^{2} + 3x + 4y = 0$
B) $x^{2} + y^{2} + 3x - 4y = 0$
C) $x^{2} + y^{2} - 3x + 4y = 0$
D) $x^{2} + y^{2} - 3x - 4y = 0$
Explanation
(d)
The coordinates of points $A$ and $B$ are (3, 0) and (0, 4) respectively
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Let the equation of circle is
$x^{2} + y^{2} + 2gx + 2fy + c = 0$ …(i)
Since, this circle passes through (0, 0), (3, 0) and (0, 4) respectively, then
$c = 0,\ g = - \frac{3}{2}$ and $f = - 2$
On putting these value in Eq. (i), we get
$x^{2} + \ y^{2} - 3x - 4y = 0$
Which is required equation of circle
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.