Q33 / 92 · NTA Abhyas (JEE Main) 2020 · Mathematics · Parabola

The focus of the conic represented parametrically by the equation $y = t^{2} + 3, x = 2 t - 1$ is

A
$(1,4)$
B
$(4,1)$
C
$(- 1,3)$
Correct answer
D
$(- 1,4)$

Solution

Given $y = t^{2} + 3, x = 2 t - 1$

Eliminating $t,$ we get,

$y = {(\frac{x + 1}{2})}^{2} + 3$
$\Rightarrow {(x + 1)}^{2} = 4 (y - 3)$
Hence, vertex: $(- 1,3)$ and focus: $(- 1,4)$

Hence, the correct answer is option: 'D'.

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