Question

Equation of line passing through mid point of intercepts made by circle $x^2+y^2-4x-6y=0$ on coordinate axes is

• A. $3x+2y-12=0$
• B. $3x+y-6=0$
• C. $3+4y-12=0$
• D. $3x+2y-6=0$

Answer 1

The correct option is D $3x+2y-6=0$

Given circle

$x^2+y^2-4x-6y=0$

On putting $y=0$ in equation of circle we get the x intercept made by circle

$x^2-4x=0$

$x(x-4)=0$

$x=0,4$

On putting $x=0$ in equation of circle we get the y intercept made by circle

$y^2-6y=0$

$y(y-6)=0$

$y=0,6$

Intercept made by circle on coordinate axes are $(4,0)$ and $(0,6)$

$\text{Equation of line through midpoint of intercepts in intercept form}$

$\frac{x}{2}+\frac{y}{3}=1$

$3x+2y=6$

$3x+2y-6=0$