Question

Equation of circle passing through the origin and making intercepts of length $10$ units and $12$ units on $x$ axis and $y$ axis respectively, can be

• A. $x^2+y^2+5x+6y=0$
• B. $x^2+y^2-10x-12y=0$
• C. $x^2+y^2+10x-12y=0$
• D. $x^2+y^2-10x+12y=0$

Answer 1

Answer: (B), (C), (D)

The correct options are
B $x^2+y^2-10x-12y=0$
C $x^2+y^2+10x-12y=0$
D $x^2+y^2-10x+12y=0$

Let the circle $x^2+y^2+2gx+2fy+c=0$ passes through $(0,0).$
Then $0+0+0+0+c=0$
$\Rightarrow c=0$

Intercept on $x$-axis :
$2\sqrt{g^2-c}=10$
$\Rightarrow g^2=5^2$
$\Rightarrow g=\pm 5$
Intercept made on $y$-axis :
$2\sqrt{f^2-c}=12$
$\Rightarrow f^2=6^2$
$\Rightarrow f=\pm 6$
$\therefore$ Required circles are $x^2+y^2\pm 10x\pm 12y=0$