Question

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

Answer 1

Latus rectum =4a=8.
`:." "a=2`.
Now, the vertex lies at distance a units from the focus.
Let the vertex be (x,y).
`:." "(x-2)^(2)+(y-3)^(2)=4`
which is the equation of locus of the vertex.