The locus of a point which divides the line segment joining the point (0,-1) and a point o…

Question

The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola $x^2=4y$, internally in the ratio $1:2$, is:

Accepted Answer

Take point P(2t, t2
) on parabola x2
 = 4y

h = $${{2t + 0} \over 3}$$ and k = $${{{t^2} - 2} \over 3}$$

$$ \Rightarrow $$ t = $${{3h} \over 2}$$ and  3k + 2 = t2

$$ \therefore $$ 3k + 2 = $${{9{h^2}} \over 4}$$

$$ \Rightarrow $$  9x2 -- 12y = 8

Solutions · 1