Question

Equation of the circumcircle of the triangle formed by the co-ordinate axes and the line 3X + 4y =24 is:

• A. $x^2+y^2-8x-6y=0$
• B. $x^2+y^2+8x-6y=0$
• C. $x^2-y^2+8x-6y=0$
• D. $x^2+y^2-8x+6y=0$

Answer 1

The correct option is A $x^2+y^2-8x-6y=0$

REF.image

$3x+4y=24\Rightarrow \frac{x}{8}+\frac{y}{6}=1$

As $\angle AOB={90}^{\circ }\Rightarrow$ AB is diameter

of circle (angle in a semicircle $={90}^{\circ }$)

$\Rightarrow$ C (mid point of AB) is the center

$\Rightarrow$ C (4,3) & AC $=\sqrt{4+9}=\sqrt{13}$ is radius

$\Rightarrow e{q}^n$ of circle : $(x-4{)}^2+(y-3{)}^2=13\Rightarrow x^2+y^2-8x-6y=0$

$\Rightarrow \left(A\right)$