StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q 28.

Expert-verifiedFound in: Page 643

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Vertex at $\left(0,0\right)$, axis of symmetry is the x-axis; containing the point $\left(2,3\right)$.

The equation of a parabola is ${y}^{2}=\frac{9}{2}x$. The points are $\left(\frac{9}{8},\frac{9}{4}\right)$ and $\left(\frac{9}{8},-\frac{9}{4}\right)$.

The graph of a parabola is :

The given vertex is at the point $\left(0,0\right)$ and the axis of symmetry is the x-axis and containing the point $\left(2,3\right)$.

The vertex is at the origin, the axis of symmetry is the x-axis and the graph contains a point in the first quadrant. The general form of the equation is

${y}^{2}=4ax$

Because the point $\left(2,3\right)$ is on the parabola, the coordinates $x=2,y=3$ must satisfy the equation of the parabola. Substitute the values, we get

${3}^{2}=4a\left(2\right)\phantom{\rule{0ex}{0ex}}9=8a\Rightarrow a=\frac{9}{8}$.

The equation will be ${y}^{2}=\frac{9}{2}x$.

The focus is at the point $\left(\frac{9}{8},0\right)$. The two points that determines the latus rectum by letting $x=\frac{9}{8}$. Then,

${y}^{2}=\frac{9}{2}x\phantom{\rule{0ex}{0ex}}{y}^{2}=\frac{9}{2}\left(\frac{9}{8}\right)\phantom{\rule{0ex}{0ex}}{y}^{2}=\frac{81}{16}\phantom{\rule{0ex}{0ex}}y=\pm \frac{9}{4}$.

The points are $\left(\frac{9}{8},\frac{9}{4}\right)$ and $\left(\frac{9}{8},-\frac{9}{4}\right)$.

The graph of a parabola is

94% of StudySmarter users get better grades.

Sign up for free