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: $\left(-1,4\right)$