IIT-JEE 2011 · Paper 2 · Mathematics Q44

MathematicsSingle correct+3 / -1Question 44 of 60

The circle passing through the point $(-1,0)$ and touching the $y$ -axis at $(0,2)$ also passes through the point

\left(-\frac32,0\right)

\left(-\frac52,2\right)

\left(-\frac32,\frac52\right)

(-4,0)

Answer and worked solution

Official answer: D

Circle touching the y-axis at (0, 2): centre $(h,2)$ , radius $|h|$ .

Through (−1, 0): $(h+1)^2+4=h^2$ , so $h=-\frac52$ , giving $\left(x+\frac52\right)^2+(y-2)^2=\frac{25}4$ .

Test (−4, 0): $\frac94+4=\frac{25}4$ ✓. (The other options fail.)

(D)

Topics:Equation of a circle

IIT-JEE 2011 · Paper 2, Mathematics question 44