JEE MAIN - Mathematics (2020 - 8th January Morning Slot - No. 9)
The locus of a point which divides the line
segment joining the point (0, –1) and a point on
the parabola, x2 = 4y, internally in the ratio
1 : 2, is :
9x2 – 3y = 2
4x2 – 3y = 2
x2 – 3y = 2
9x2 – 12y = 8
Explanation
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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
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