Question

The focus of a parabola is (−5,−1) and the directrix is y=−3.

What is an equation of the parabola?

Answer 1

The equation of parabola= 1/4(x+5)²-2.

Explanation:

The focus of parabula is ( -5,-1) and the directrix is y=−3.

The focus and directrix are equi-distance from vertex.

so vertex : (-5,-2)

The equation of parabola : y = a(x-h)²+k

The distance between focus and vertex (p) = 1

a=1/4p= 1/4(1)=1/4

Putting value of vertex and value of a into above formula.

y = 1/4 (x+5)²-2 is the equation of parabola.

Answer 2

The equation of parabola:
`y=(1)/(4)(x+5)^2-2`

Explanation:

The focus of a parabola is (−5,−1) and the directrix is y=−3

Focus and Directrix are equi-distance from vertex.

Directrix: y=-3 and Focus: (−5,−1)

Thus, The Vertex: (−5,−2)

Equation of parabola:
`y=a(x-h)^2+k`

Distance between Focus and Vertex (p) = 1

`a= (1)/(4p)=(1)/(4)`

Substitute vertex and value of a into formula

Hence, The equation of parabola:
`y=(1)/(4)(x+5)^2-2`