JEE Main 2014 · 6 Apr · Shift 1 · Mathematics Q81

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MathematicsSingle correct+4 / -1Question 81 of 90

Let C be the circle with centre at $(1,1)$ and radius $=1$ . If T is the circle centred at $(0,y)$ , passing through origin and touching the circle C externally, then the radius of T is equal to :

\dfrac12

\dfrac14

\dfrac{\sqrt3}{\sqrt2}

\dfrac{\sqrt3}{2}

Answer and worked solution

Official answer: B

T passes through the origin, so its radius is $|y|$ ; take $y>0$ . External contact: the distance between centres is the sum of the radii:
$\sqrt{1+(y-1)^2}=1+y\implies2-2y+y^2=1+2y+y^2\implies y=\frac14.$

Topics:Equation of a circle

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JEE Main 2014 · 6 Apr · Shift 1, Mathematics question 81