Question

The equation of a circle with origin as centre passing through the vertices of an equilateral triangle whose median is of length 3a is

• A. $x ^ { 2 } + y ^ { 2 } = 9 a ^ { 2 }$
• B. $x ^ { 2 } + y ^ { 2 } = 16 a ^ { 2 }$
• C. $x ^ { 2 } + y ^ { 2 } = a ^ { 2 }$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Since the triangle is equilateral, therefore centroid of the triangle is the same as the circumcentre and radius of the circum-circle $= \frac { 2 } { 3 }$ (median) $= \frac { 2 } { 3 } ( 3 a ) = 2 a$

$[ \because$Centroid divides median in ratio of 2 : 1]

Hence, the equation of the circum-circle whose centre is (0, 0) and radius 2a is $x ^ { 2 } + y ^ { 2 } = ( 2 a ) ^ { 2 }$

$\Rightarrow x ^ { 2 } + y ^ { 2 } = 4 a ^ { 2 }$