Question

Find the equation of the circle with radius $5$ whose centre lies on x-axis and passes through the point $(2,3)$.

• A. $x^2+y^2+4x-20=0$
• B. $x^2+y^2+4x-21=0$
• C. $x^2+y^2+2x-21=0$
• D. $x^2-y^2+4x-21=0$

Answer 1

Answer: (B)

$x^2+y^2+4x-21=0$

We have,

$radius=5$

And the centre lies on $x-axis$.

Let the centre $(h,0)$

Therefore,

$(x-h{)}^2+y^2=5^2$

Since, the circle passes through the point $(2,3)$

Then,

$(2-h{)}^2+3^2=25$

$(2-h{)}^2=16$

$2-h=4$

$h=-2$

So, the centre will be $(-2,0)$

Therefore, the equation of the circle

$(x+2{)}^2+y^2=25$

$x^2+4+4x+y^2=25$

$x^2+y^2+4x-21=0$

Hence, this is the answer.