Question

A rod PQ of length 2a slides with its ends on the axes the locus of the circum-centre of $\Delta$ OPQ is

• A. $x^2$ + $y^2$ = 2$a^2$
• B. $x^2$ + $y^2$ = 4$a^2$
• C. $x^2$ + $y^2$ = 3$a^2$
• D. $x^2$ + $y^2$ = $a^2$

Answer 1

The correct option is D $x^2$ + $y^2$ = $a^2$

Let C (h, k) be a point in the locus
C(h, k) is mid point of PQ $\Rightarrow$ P(2h, 0), Q(0, 2k)
PQ = 2a $\Rightarrow P{Q}^2=4a^2$ $\Rightarrow 4h^2+4k^2=4a^2$ $\Rightarrow h^2+k^2=a^2$
Locus of (h, k) is $x^2$ + $y^2$ = $a^2$