Answer:
Step-by-step explanation:
The equation of ellipse is given as:
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) (1)
Now, from the given information, The ellipse passes through (0, 58), (0, -58), (21, 29), thus equation (1) becomes:
\(\frac{0}{a^2}+\frac{(58)^2}{b^2}=1\)
⇒\(b^2=(58)^2\)
⇒\(b^2=3364\)
Also, \(\frac{(21)^2}{a^2}+\frac{(29)^2}{(58)^2}=1\)
⇒\(\frac{(21)^2}{a^2}=1-\frac{841}{3364}\)
⇒\(\frac{(21)^2}{a^2}=\frac{3}{4}\)
⇒\(a^2=\frac{4(441)}{3}\)
⇒\(a^2=588\)
Now, substituting the values of \(a^2 and b^2\) in the equation (1), we have
\(\frac{x^2}{588}+\frac{y^2}{3364}=1\)
which is the required equation for ellipse.
