Question

determine whether the equation 4x^2 - 9y^2 = 36 defines as a function of x

Answer 1

In that question... just replace (-x) or (-y) to the equation..
The one that you can get the same answer will be its function...

-- am i right @hartnn ?

Answer 2

the equation is a function of x

Answer 3

4x² + 9y² = 36

Subtract 4x² from both sides:

9y² = 36 - 4x²

Divide both side by 9:

y² = {36 - 4x²}/9

Factor out (4/9) on the right:

y² = {4/9}{9 - x²}

Take the square root of both sides:

y = (2/3)sqrt{9 - x²}

y = -(2/3)sqrt{9 - x²}

Check by starting with the original equation and substituting both values for y:

4x² + 9y² = 4x² + 9{(2/3)sqrt{9 - x²}}² = 4x² + 9{(4/9){9 - x²} = 4x² + 4{9} - 4x² = 36

4x² + 9y² = 4x² + 9{-(2/3)sqrt{9 - x²}}² = 4x² + 9{(4/9){9 - x²} = 4x² + 4{9} - 4x² = 36

Answer 4

9y² = 36 - 4x² = 4(9 - x²)

y² = 4/9*(9 - x²)

√y² =√ [4/9*(9 - x²)]

y = ±2/3√(9 - x²)

I don't know where you got that ±√(x - 1)

Your equation is an ellipse.
Divide all by 36
x²/9 + y²/4 = 1 the center is (0, 0) the major axis is "x" with a length of 3 while the minor axis is y with a length of 2.