Chapter 10.5, Problem 12AYU

To determine

The graph of each equation without completing their squares: $2y²-3y+3x=0$.

Answer to Problem 12AYU

Parabola.

Explanation of Solution

Given:

$2y²-3y+3x=0$

Formula used:

$Ax²+Cy²+Dx+Ey+F=0$

where $A$ and $C$ are not both equal to zero:

a. Defines a parabola if $AC=0$.

b. Defines an ellipse (or a circle) if $AC>0$.

c. Defines a hyperbola if $AC<0$.

Calculation:

Consider the given equation $2y²-3y+3x=0$.

$A=0\text{ and }C=2$; $AC=\left(2\right)\left(0\right)=0$

Since $AC=0$, the equation defines a parabola.