Shortest distance from a point to a line-
write an equation for the parabola with vertex at (3,-5) and going through (1,-8)

The equation of parabola in vertex form is

Solution:

Given that parabola with vertex (3, -5) and going through point (1, -8)

To find : equation of parabola

The equation of parabola in vertex form is given as:

 ----- eqn 1

where (h, k) are the coordinates of the vertex

here (h, k) = (3, −5)

Substituting the values in above formula, we get

 ----- eqn 2

The given equation of parabola passes through (1, -8)

Substituiting (x, y) = (1, -8) in eqn 2 we get,

Now substitute the value of "a" in eqn 2,

Thus the equation of parabola in vertex form is found