Chapter 10: Q. 9 (page 654)

For the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$ , the vertices are the points _ and _.

Short Answer

Expert verified

For the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$ , the vertices are the points $(0, - 5) a n d (0, 5)$ .

Step by step solution

Step 1. Given Information.

We want to fill the gap in the given equation with the missing terms.

Step 2. Method to find:

We know that

If an ellipse is given with the following equation:

$\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} = 1$

where $a > b$ , then it is centred at the origin, the major axis is the y-axis and the parameters $a a n d b$ represent its width $2 a$ and its height $2 b$ .

Since the vertices lie on the major axis and the segment connecting them is the width of the ellipse, then it is $2 a$ long.

Therefore, the vertices are the points $(0, - a) a n d (0, a)$

Step 3. Solution:

The following equation is given

$\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$

then by comparing it to the equation of an ellipse given in Step 2. we can see that

Since $2^{2} = 4$ and because $25 > 4 \Leftrightarrow 5 > 2$

Therefore, the vertices are points:

$V_{1} = (0, - 5) a n d V_{2} = (0, 5)$

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For the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$ , the vertices are the points _ and _.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Method to find:

Step 3. Solution:

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For the ellipse x24+y225=1, the vertices are the points _____ and _____.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Method to find:

Step 3. Solution:

One App. One Place for Learning.

Most popular questions from this chapter

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For the ellipse $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$ , the vertices are the points _ and _.