Question

If the focus of a parabola is (2, 3) and its latus rectum is 8, then the locus of the vertex of the parabola is

• A. (0, 3)
• B. $(x-2{)}^2+(y-3{)}^2=4$
• C. $(y-3{)}^2=8(x-2)$
• D. $x-2y+4=0$

Answer 1

The correct option is B

$(x-2{)}^2+(y-3{)}^2=4$

Let 'a' be the dictance between the focus and the vertex. Then, latus rectum =4a
$\Rightarrow 4a=8\Rightarrow a=2$
Since the focus is fixed i.e., (2, 3), The vertex is the locus of all points which are at a dictance of 2 units from the focus.
$(x-2{)}^2+(y-x{)}^2=2^2\Rightarrow (x-2{)}^2+(y-3{)}^2=4$