Question

# Find an equation of the conic described.graph the equation. Parabola:focus(-1,4.5) vertex (-1,3).

Equations
Find an equation of the conic described.graph the equation. Parabola:focus(-1,4.5) vertex (-1,3).

2021-05-18

Step 1
The focus of the parabola is given as (-1,4.5)
The vertex of the parabola is given as (-1,3)
The axis of the parabola is given as,
x=-1
Hence, the given parabola is vertical parabola,
Step 2
If the axis of the parabola is parallel to y-axis and the vertex of the parabola is (h,k) then the general equation of the parabola is given as,
$$(x-h)^{2}=4a(y-k)$$
a=4.5-3
=-1.5
Putting the values, we get
$$(x-(-1))^{2}=4*(1.5)(y-3)$$
$$(x+1)^{2}=6(y-3)$$
$$x^{2}+1+2x=6y-18$$
$$x^{2}+2x-6y+19=0$$
Therefore, the required equation of the parabola is $$x^{2}+2x-6y+19=0$$