Question

The equation of the circle of radius $5$ with centre on x-axis and passing through the point $(2,3)$ is

• A. $x^2+y^2-12x+11=0$
• B. $x^2+y^2-4x-21=0$
• C. $x^2+y^2+12x+11=0$
• D. $x^2+y^2-4x+21=0$

Answer 1

The correct option is A $x^2+y^2-12x+11=0$

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

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

Let the center of given circle be (k,0).

Then, equation of circle,

$\to$ $(x-k{)}^2+(y-0{)}^2=5^2$

Since circle passes through (2,3),

$\to$ $(2-k{)}^2+3^2=5^2$

Solving we get, k = {6,-2}

So, Possible equations are,

(i) $(x-6{)}^2+y^2=25$ $\to$ $x^2+y^2-12x+11=0$

(ii) $(x+2{)}^2+y^2=25$ $\to$ $x^2+y^2+4x-21=0$

Hence, (A) and (B) are correct answers.