Question

If a parabola $y^2=16x$ is translatated to the coordinate $P(1,0),$ then the coordinates of it's focus is

• A. $S(3,0)$
• B. $S(1,0)$
• C. $S(5,0)$

Answer 1

The correct option is C $S(5,0)$

Given the parabola $y^2=16x$.
Focus of given parabola is given by $(4,0)$ and the vertex is $(0,0).$
According to the question, this parabola is translated to point $P(1,0)$
$\Rightarrow$ Vertex will be shifted by $1$ unit horizontally without shifting of axis.
$\Rightarrow$ New vertex will be $Q(1,0).$
Also, the new equation of parabola becomes $y^2=16(x-1)$
Thus. the focus will also get shifted by one unit.
$\because$ Coordinates of new focus will be $S(5,0).$