# What is the vertex form of the equation of the parabola with a focus at (11,28) and a directrix of y=21 ?

The equation of parabola in vertex form is $y = \frac{1}{14} {\left(x - 11\right)}^{2} + 24.5$
The Vertex is equuidistant from focus(11,28) and directrix (y=21). So vertex is at $11 , \left(21 + \frac{7}{2}\right) = \left(11 , 24.5\right)$
The equation of parabola in vertex form is $y = a {\left(x - 11\right)}^{2} + 24.5$. The distance of vertex from directrix is $d = 24.5 - 21 = 3.5$ We know, $d = \frac{1}{4 | a |} \mathmr{and} a = \frac{1}{4 \cdot 3.5} = \frac{1}{14}$.Since Parabola opens up, 'a' is +ive.
Hence the equation of parabola in vertex form is $y = \frac{1}{14} {\left(x - 11\right)}^{2} + 24.5$ graph{1/14(x-11)^2+24.5 [-160, 160, -80, 80]}[Ans]