Question

Write the standard form of an equation of an ellipse subject to the given conditions.

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The standard form of the equation of an ellipse with major axis on the y axis is given as:

$\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1$

Where (h, k) is the center of the ellipse, (h, k ± a) is the major axis, (h ± b, k) is the minor axis, (h, k ± c) is the foci and c² = a² - b²

Since the minor axis is at (37,0) and (-37,0), hence k = 0, h = 0 and b = 37

Also, the foci is at (0,5) and (0, -5), therefore c = 5

Using c² = a² - b²:

5² = a² - 37²

a² = 37² + 5² = 1369 + 25

a² = 1394

Therefore the equation of the ellipse is:

$\frac{x^2}{1369}+ \frac{y^2}{1394} =1$