what is an equation of a parabola with a with the given vertex and focus vertex: (-2, 5) focus: (-2, 6)

Step-by-step explanation:

As the vertex (-2,5) and focus (-2,6) share same abscissa i. e. - 2, parabola has axis of symmetry as x=-2 or x+2=0

Hence, equation of parabola is of the type (y-k) = a (x-h) 2, where (h, k) is vertex. Its focus then is (h, k+14a)

As vertex is given to be (-2,5), the equation of parabola is

y-5=a (x+2) 2

as vertex is (-2,5) and parabola passes through vertex.

and its focus is (-2,5+14a)

Therefore 5+14a=6 or 14a=1 i. e. a=14

and equation of parabola is y-5=14 (x+2) 2

or 4y-20 = (x+2) 2=x2+4x+4

or 4y=x2+4x+24