find two explicit functions by solving the equation for y in terms of x

9x² + 16y² = 144

 

Subtract 9x2 from both sides

16y² = 144 - 9x²

 

Divide both sides by 16

y² = (144 - 9x²)/16

 

Take the square root of both sides. Since there are two possibilities we create two functions in doing so:

 

y = (144 - 9x²)^1/2/4  and  y = -(144 - 9x²)^1/2/4

 

.