The graph of 5x - 9y^2 = 12 - 4y is the graph of a(n)______.
a. circle
b. ellipse
c. hyperbola
d. parabola
C?
circle, ellipse and hyperbola all need x^2 and y^2 terms.
You have x = ay^2 + by + c which is a parabola
Thanks!
To determine the shape of the graph, we need to analyze the equation. The given equation is 5x - 9y^2 = 12 - 4y.
To simplify the equation, let's rearrange it by moving all terms to one side:
5x + 4y - 9y^2 = 12
Now, let's look at the equation in terms of the variables x and y. Since the equation includes both x and y terms, it suggests that the graph might be a conic section.
To identify the conic section, we can check the coefficient of y^2. In this case, the coefficient is -9. Based on the coefficient's value, we can classify the graph:
1. If the coefficient of y^2 is positive, the conic section is an ellipse.
2. If the coefficient of y^2 is negative, the conic section is a hyperbola.
3. If the coefficient of y^2 is zero, the conic section is a parabola.
In our equation, the coefficient of y^2 is -9, which is negative. Therefore, the graph of the equation 5x - 9y^2 = 12 - 4y is a hyperbola.
So the correct answer is C.