Question

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

• A. $\left(1,4\right)$
• B. $\left(4,1\right)$
• C. $\left(- 1,3\right)$
• D. $\left(- 1,4\right)$

Answer 1

Answer: (D)

Given $y=t^{2}+3,x=2t-1$
Eliminating $t,$ we get,
$y=\left(\frac{x + 1}{2}\right)^{2}+3$
$\Rightarrow \left(x + 1\right)^{2}=4\left(y - 3\right)$
Hence, vertex: $\left(- 1,3\right)$ and focus: $\left(- 1,4\right)$