Find the lengths of the major and minor axes for the ellipse. $25 x ^ { 2 } + y ^ { 2 } = 25$
A) major axis: $5$
, minor: $2$
B) major axis: $5$
, minor: $\sqrt { 5 }$
C) major axis: $25$
, minor: $2 \sqrt { 10 }$
D) major axis: $10$
, minor: $2$
E) none of these

Question

Quizplus · Accepted Answer

We can put the given equation in standard form of ellipse by dividing both sides by 25 to get $\frac{x^2}{1}+\frac{y^2}{25}=1$. This gives us the equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, where $a=1$ and $b=5$. Thus, the length of the major axis is $2a=2$ and the length of the minor axis is $2b=10$. Therefore, the answer is D.

Find the Lengths of the Major and Minor Axes for the Ellipse