Final answer:
To find the lengths of the major and minor axes of the ellipse -56+9y²=10x-x², we need to rewrite the equation in standard form and compare it with the standard form equation. Then, we can determine the lengths of the major and minor axes as 2a and 2b, respectively.
Step-by-step explanation:
The given equation of the ellipse is -56+9y²=10x-x². To find the lengths of the major and minor axes of the ellipse, we need to rewrite the equation in standard form:
Dividing the equation by -56, we get 1 - (9y²/56) = (10x-x²)/(-56)
Rearranging the equation, we have (9y²/56) - (10x-x²)/56 = 1
Comparing this equation with the standard form: (x²/a²) + (y²/b²) = 1, we can see that a² = 56 and b² = 56/9.
Therefore, the lengths of the major and minor axes of the ellipse are:
- The major axis = 2a = 2√56
- The minor axis = 2b = 2√(56/9)