Question

4. Use your answer to Problem 3 to find the equation of the ellipse for each of the situations below.
a. An ellipse centered at the origin with x-intercepts (−2,0), (2,0) and yy-intercepts (0,8), (0, −8)
b. An ellipse centered at the origin with x-intercepts (−√5, 0), (√5, 0) and yy-intercepts (0,3), (0, −3)

Answer 1

Answer:

Step-by-step explanation:

(a)Ellipse centered at the origin with x-intercepts (−2,0), (2,0) and yy-intercepts (0,8), (0, −8)

as the length of  x intercept is smaller than y intercept therefore it is a vertical Ellipse of the form

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

length of major axis $=2a=2\times 8=16$

Length of minor axis$=2b=2times 2=4$

thus Equation of Ellipse is

$\frac{x^2}{2^2}+\frac{y^2}{8^2}=1$

(b)x intercept is $(-\sqrt{5},0) (\sqrt{5},0)$

Y intercept is (0,3) (0,-3)

here also Y intercept is greater than x intercept thus it is also a vertical ellipse

length of major axis $=2a=2\times 3=6$

Length of minor axis$=2b=2\times \sqrt{5}=2\sqrt{5}$

thus Equation of Parabola is

$\frac{x^2}{\sqrt{5}^2}+\frac{y^2}{3^2}=1$