Find an equation of the conic described;graph the equation. Parabola:focus

Annette Arroyo

Annette Arroyo

Answered question

2021-09-10

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

Answer & Explanation

Alix Ortiz

Alix Ortiz

Skilled2021-09-11Added 109 answers

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,
(xh)2=4a(yk)
a=4.5-3
=-1.5
Putting the values, we get
(x(1))2=4(1.5)(y3)
(x+1)2=6(y3)
x2+1+2x=6y18
x2+2x6y+19=0
Therefore, the required equation of the parabola is x2+2x6y+19=0

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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