Question

Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 16.

Answer 1

Let us assume then that the center is the origin.  If the major axis is 18, then a = 9 and a^2=81.  If the minor axis is 16, then b = 8 and b^2=64.  Now you can write the equation.  Remember that this ellipse is vertical and so a^2 goes under y^2

Answer 2

Answer:

x²/64 + y²/81 = 1

Step-by-step explanation:

Standard form of an equation for the ellipse is $\frac{x^{2} }{a^{2}}+\frac{y^{2} }{b^{2} }=1$

Here b is the length of vertical major axis = 9

and minor axis of length a = 8

Therefore the equation of the ellipse will be

$\frac{x^{2} }{8^{2} }+\frac{y^{2} }{9^{2} } =1$

$\frac{x^{2} }{64}+\frac{y^{2} }{81}=1$

So the answer is x²/64 + y²/81 = 1