Question

what is the length of the major axis of the conic section (x+2)^2/64+(y-1)^2/81=1

Answer 1

Answer: The length of the major axis = 18 units.

Step-by-step explanation:

For equation ellipse: $\dfrac{(x-a)^2}{m^2}+\dfrac{(y-b)^2}{n^2}=1$

If n>m , then length of major axis = 2n

Otherwise 2m

Given equation:

$\dfrac{(x+2)^2}{64}+\dfrac{(y-1)^2}{81}=1\ \text{ ,which is an ellipse.}\\\\\Rightarrow\ \dfrac{(x+2)^2}{8^2}+\dfrac{(y-1)^2}{9^2}=1$

9>8

So, the length of the major axis = 2(9) = 18 units.