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)
Hello, ccdalamp!
The center of the ellipse is the origin: $\displaystyle (0,\,0)$Find the vertices of the ellipse: .$\displaystyle \frac{x^2}{4} + \frac{y^2}{25}\;=\;1$
Choices: . $\displaystyle a)\;V(0,\,\pm5)\qquad b)\;V(0,\,\pm25) \qquad c)\; V(\pm2,\,0)\qquad d)\;V(\pm4,\,0)$
The denominator of the $\displaystyle x$-fraction is: .$\displaystyle a^2 = 4\quad\Rightarrow\quad a = \pm 2$
The denominator of the $\displaystyle y$-fraction is: .$\displaystyle b^2 = 25\quad\Rightarrow\quad b = \pm5$
Since the larger denominator is "under the $\displaystyle y$", 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: .$\displaystyle (0,\,\pm5)$