Question

Cal-2 help required.Screenshot attached below.

Answer 1

For 27 (a), see http://www.mathwarehouse.com/ellipse/equation-of-ellipse.php

the equation of an ellipse is
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} =1 \]

a is 1/2 of the major axis, or the distance from the origin to one end of the major axis. In other words, a = 3
similarly , b = distance from the origin to the end of the minor axis = 2

Answer 2

for 27 (b) see http://www.mathwarehouse.com/ellipse/focus-of-ellipse.php

here they tell you the major axis is 26, so a is 1/2 of this or a= 13
you need to find b (and then use a^2 and b^2 in the equation of an ellipse)

if we call the distance of the focus from the origin c, we have the formula
c^2 = a^2 - b^2
solve for b^2

b^2= a^2 - c^2