Answer:
The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]
Step-by-step explanation:
The standard form of the equation of an ellipse with center (0 , 0) is
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex] , where
∵ The ellipse is centered at the origin
∴ The center of it is (0 , 0)
∵ It has foci at (± 8 , 0)
- The coordinates of the foci are (± c , 0)
∴ c = ±8
∵ It has Vertices at (± 17 , 0)
- The coordinates of the vertices are (± a , 0)
∴ a = ±17
∵ c² = a² - b²
- Substitute the values of c and a to find b
∴ (8)² = (17)² - b²
∴ 64 = 289 - b²
- Add b² to both sides
∴ b² + 64 = 289
- Subtract 64 from both sides
∴ b² = 225
- Take √ for both sides
∴ b = ± 15
∵ The equation of the ellipse is [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]
- Substitute the values of a and b in it
∴ [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex] ⇒ [tex]\frac{x^{2}}{289}+\frac{y^{2}}{225}=1[/tex]
∴ The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]
