Question

The equation $y^2 + 3 = 2(2x + y)$ represents a parabola with the vertex at

• A. $\left(\frac{1}{2}, 1\right)$ and axis parallel to y-axi
• B. $\left(1,\frac{1}{2}\right)$ and axis parallel to x-axis
• C. $\left(\frac{1}{2}, 1\right)$ and focus at $\left(\frac{3}{2}, 1\right)$
• D. $\left(1,\frac{1}{2}\right)$ and focus at $\left(\frac{3}{2}, 1\right)$

Answer 1

Answer: (C)

$\left(\frac{1}{2}, 1\right)$ and focus at $\left(\frac{3}{2}, 1\right)$

Answer 2

The given equation can be rewritten as
$\left(y-1\right)^{2}=4\left(x-\frac{1}{2}\right)$ which is a parabola
with its $vertex\left(\frac{1}{2}, 1\right)$ axis along the line
$y = 1$, hence axis parallel to x-axis.
Its focus is $\left(\frac{1}{2}+1, 1\right)$, i.e., $\left(\frac{3}{2}, 1\right)$