Question

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

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

Answer 1

Answer: (B), (C)

The correct options are
B $(\frac{1}{2},1)$ and axis parallel to $x$-axis
C $(\frac{1}{2},1)$ and focus at $(\frac{3}{2},1)$

$y^2+3=2(2x+y)$ represents parabola.

$y^2+3=4x+2y$

$y^2-2y+3=4x$

$y^2-2y+1+3=4x+1$

$(y-1{)}^2=4x-2$

$(y-1{)}^2=4(x-\frac{1}{2})$

So, the vertex of parabola$=(\frac{1}{2},1)$ and axis is parallel to x axis.

$a=1$

Focus$=(\frac{1}{2}+1,1)$

$=(\frac{3}{2},1)$