Isolate the terms involving y on the left side of the equation

OlmekinjP

OlmekinjP

Answered question

2021-10-02

Isolate the terms involving y on the left side of the equation:
y2+2y+12x23=0.
Then write the equation in an equivalent form by completing the square on the left side.

Answer & Explanation

firmablogF

firmablogF

Skilled2021-10-03Added 92 answers

Step 1
The given equation is y2+2y+12x23=0.
The terms of y are isolated on the left side as follows.
y2+2y=12x+23
Step 2
By completing the square, the equivalent form of the above equation is obtained as follows.
y2+2y=12x+23
(y+1)21=12x+23
(y+1)2=12x+24
(y+1)2=12(x2)
(y(1))2=12(x2)
This is the equation of the parabola with vertex (2,-1) opening leftwards.

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