Question

A circle of radius $5$ has its centre on the negative x-axis and passes through the point $(2,3)$. The intercept made by the circle on the y - axis is

• A. $10$
• B. $2\sqrt{21}$
• C. $2\sqrt{11}$
• D. imaginary y-intercept

Answer 1

Answer: (B)

$2\sqrt{21}$

Let the centre of the circle is $(-h,0)$

The distance between centre and the point (2,3) is the radius of the circle

$(2+h{)}^2+9=25⟹2+h=4⟹h=2$

Now the equation of the circle is $(x+2{)}^2+y^2=25$

Above circle intersects y axis at $(0,\sqrt{21})$ and $(0,-\sqrt{21})$

The intercept made by the circle on the y - axis is $2\sqrt{21}$