Questions: Which equation represents the graph? A) (6-3p)/6-(6-2y)/2=1 C) x=-y^2-2 B) (x-2)/4+(6-3p)/36=1 D) y=2x^3-2

Transcript text: Which equation represents the graph? A) $\frac{(6-3 p}{6}-\frac{6-2 y}{2}=1$ C) $x=-y^{2}-2$ B) $\frac{(x-2)}{4}+\frac{6-3 p}{36}=1$ D) $y=2 x^{3}-2$

Solution

Solution Steps

Step 1: Identify the type of conic section

The graph shown is an ellipse, as it is an elongated circle.

Step 2: Determine the standard form of an ellipse

The standard form of an ellipse centered at the origin is: \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] where $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively.

Step 3: Analyze the given options

We need to match the given options to the standard form of an ellipse:

Option A: $\frac{x^2}{4} + \frac{y^2}{36} = 1$
Option B: $\frac{x^2}{36} + \frac{y^2}{4} = 1$
Option C: $x = y^2 - 2$
Option D: $y = 2x^2 - 2$

Step 4: Compare the graph with the options

The graph shows a vertical ellipse, which means the major axis is along the y-axis. This corresponds to the form where the larger denominator is under $y^2$.