Question

question 2 of 10 which conic section is represented by the equation shown below? 9x + 4y²+18x = 16 a. ellipse b. parabola c. hyperbola d. circle

Explanation:

Step1: Combine like - terms for x

Combine $9x$ and $18x$ in the equation $9x + 4y^{2}+18x=16$. We get $27x + 4y^{2}=16$, which can be rewritten as $27x=16 - 4y^{2}$ or $x=\frac{16 - 4y^{2}}{27}=-\frac{4}{27}y^{2}+\frac{16}{27}$.

Step2: Analyze the form of the equation

The general form of a parabola is $x = ay^{2}+by + c$ (when it opens horizontally) or $y=ax^{2}+bx + c$ (when it opens vertically). Our equation $x=-\frac{4}{27}y^{2}+\frac{16}{27}$ is in the form $x = ay^{2}+c$ where $a =-\frac{4}{27}$ and $b = 0$, $c=\frac{16}{27}$.

Answer:

B. Parabola