Answer:
The equation of parabola is standard form is [tex]x=\left(y+4\right)^2+2[/tex]
Step-by-step explanation:
Given equation of parabola is,
[tex]y^2+8y-x+18=0[/tex]
In order to find the equation of parabola in standard form, eliminate x from left side of equation and use completing square method to find the equation.
First step is to add x on both side of equation.
[tex]y^2+8y-x+18+x=0+x[/tex]
[tex]y^2+8y+18=x[/tex]
Rewriting,
[tex]x=y^2+8y+18[/tex]
Now applying completing square method as follows.
Following are the steps for calculation of this method.
Find the last term of above equation by using below formula,
[tex]Last\:term\:of\:square=\left(\dfrac{coefficient\:of\:y}{2}\right)^{2}[/tex]
Now coefficient of y is 8.
[tex]\therefore Last\:term\:of\:square=\left(\dfrac{8}{2}\right)^{2}[/tex]
Simplifying,
[tex]Last\:term\:of\:square=\left(4\right)^{2}[/tex]
[tex]Last\:term\:of\:square=16[/tex]
Second step is to add and subtract the last term.
[tex]x=y^2+8y+18+16-16[/tex]
Rewriting,
[tex]x=y^2+8y+16+18-16[/tex]
Since [tex]\left(a+b\right)^{2}=a^{2}+2ab+b^{2}[/tex]
Using above formula,
[tex]x=\left(y+4\right)^{2}+2[/tex]
Therefore, the equation of parabola in standard form is [tex]x=\left(y+4\right)^{2}+2[/tex]
