Question

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

Answer 1

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