Question

The equation of the circle passing through the origin and making intercept $4,5$ on the positive coordinates axes is

• A. $x^2+y^2-4x+5y=0$
• B. $x^2+y^2-4x-5y=0$
• C. $x^2+y^2+4x+5y=0$
• D. `$x^2+y^2+4x-5y=0$

Answer 1

The correct option is B $x^2+y^2-4x-5y=0$

For a circle with center (a,b) and radius r,

Equation is $(x-a{)}^2+(y-b{)}^2=r^2$

Their can be two scenarios for given conditions as depicted in above figures.

For (A),

Center = $(2,\frac{5}{2})$

Radius = $\sqrt{2^2+(\frac{5}{2}}{)}^2=\frac{\sqrt{41}}{2}$

So, Equation of circle,

$\to$ $(x-2{)}^2+(y-\frac{5}{2}{)}^2=\frac{41}{4}$

$\to$ $x^2+y^2-4x-5y=0$

Similarly, For (B),

Equation of circle,

$\to$ $(x-\frac{5}{2}{)}^2+(y-2{)}^2=\frac{41}{4}$

$\to$ $x^2+y^2-4y-5x=0$

Hence, (B) is the correct answer.