Question

The radius of the largest circle inscribed in the ellipse x2/16 + y2/4 = 1 and having centre at (1, 0) is

(a) 11/3

(b) √11/3

(c) 7/3

(d) √7/3

Answer 1

Correct option**(b) √11/3**

Explanation :

See Fig. Since the circle is to be largest, it must touch the ellipse (internally) at some point, say, P(4 cos *θ, 2sinθ). The tangent to the ellipse P is x cos θ/4 + ysecθ/2 = 1*

whose slope is (-1/2) cotθ . Also the line joining (1, 0) and P is perpendicular to the tangent. So

The radius of the circle is