Q:

Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 10. (5 points)x squared divided by 5 plus y squared divided by 8 = 1x squared divided by 25 plus y squared divided by 64 = 1x squared divided by 8 plus y squared divided by 5 = 1x squared divided by 64 plus y squared divided by 25 = 1

Accepted Solution

A:
Answer:[tex]\frac{x^2}{25}+\frac{y^2}{64}=1[/tex]Step-by-step explanation:If the ellipse has a vertical major axis of length 16, then[tex]2a=16[/tex][tex]\Rightarrow a=8[/tex]If the ellipse has the length of the minor axis to be 10, then;[tex]2b=10[/tex][tex]\Rightarrow b=5[/tex]The equation of the ellipse is given by;[tex]\frac{x^2}{b^2}+\frac{y^2}{a^2}=1[/tex]Thus;[tex]\frac{x^2}{5^2}+\frac{y^2}{8^2}=1[/tex][tex]\frac{x^2}{25}+\frac{y^2}{64}=1[/tex]