• Jul 10th 2007, 07:39 PM
ccdalamp
Find the vertices of the ellipse x2(square)/4 + y2(square)/25=1

Choices
a. V(0,+5)
b. V(0,+25)
c. V(+2.0)
d. V(+4,0)
• Jul 10th 2007, 09:06 PM
Soroban
Hello, ccdalamp!

Quote:

Find the vertices of the ellipse: . $\frac{x^2}{4} + \frac{y^2}{25}\;=\;1$

Choices: . $a)\;V(0,\,\pm5)\qquad b)\;V(0,\,\pm25) \qquad c)\; V(\pm2,\,0)\qquad d)\;V(\pm4,\,0)$

The center of the ellipse is the origin: $(0,\,0)$

The denominator of the $x$-fraction is: . $a^2 = 4\quad\Rightarrow\quad a = \pm 2$

The denominator of the $y$-fraction is: . $b^2 = 25\quad\Rightarrow\quad b = \pm5$

Since the larger denominator is "under the $y$", the major axis is vertical.
. . The vertices are always the ends of the major axis.

Hence, the vertices are 5 units above and below the center: . $(0,\,\pm5)$