Question

The locus of the point which divides the double ordinate of the parabola $y^2=6ax$ in the ratio $5:6,$ is

• A. $100y^2=6ax$
• B. $144y^2=6ax$
• C. $121y^2=6ax$
• D. $\frac{y^2}{121}=6ax$

Answer 1

The correct option is C $121y^2=6ax$

Let the point $P\equiv (h,k)$ divides the double ordinate with end points $A\equiv (x,y)$ and $B\equiv (x,-y)$ in the ratio $5:6.$
Then, $h=\frac{6x+5x}{11}$
$\Rightarrow x=h\cdots \left(i\right)$
and $k=\frac{6y-5y}{11}$
$\Rightarrow y=11k\cdots \left(ii\right)$

Putting $\left(i\right)$ and $\left(ii\right)$ in parabola $y^2=6ax,$ we get
$(11k{)}^2=6a(h)$
$\Rightarrow 121k^2=6ah$
Hence, locus of the point is $121y^2=6ax$