Question

lf $A(O,4)$ , $B(6,0)$ and $O$ be the origin. $A$ point $P$ moves such that area of $\Delta POA$ is twice the area of $\Delta POB$, then the locus of $P$ is:

• A. $x^2+9y^2=0$
• B. $9x^2+y^2=0$
• C. $x^2-9y^2=0$
• D. $9x^2-y^2=0$

Answer 1

Answer: (C)

$x^2-9y^2=0$

$\Delta POA,$
$(h,k),(0,4),(0,0)$

${\Delta }_1=\left|\frac{h(4-0)+0+0}{2}\right|$

$\Delta POB$
$(h,k),(6,0),(0,0)$

${\Delta }_2=\left|\frac{h(0-0)+6(0-k)}{2}\right|$

${\left|2h_1\right|}^2=2^2(3k{)}^2$ $(\therefore {\Delta }_1=2{\Delta }_2)$
$h^2=9k^2$
$x^2-9y^2=0$