Question

The equation of parabola with vertex (-2, 1) and focus (-2, 4) is​

Answer 1

Given:

Vertex = ( h,k ) = ( -2,1 )

Focus = ( -2,4 )

To find:

We have to find the equation of parabola for given vertex and focus

Solution:

When vertex (h,k) is known

$(x-h)^{2}=4a(y-k)$  for vertical parabola

Here x = -2 is the vertical line on which focus and vertex lies

So the parabola is vertical

a = 4-1 = 3

So equation is

$(x+2)^{2} = 4.3(y-1)$

$(x+2)^{2} = 12(y-1)$

The equation of required parabola is $(x+2)^{2} = 12(y-1)$

Answer 2

Answer:

The right answer in picture