Question

Find an equation in standard form for the ellipse with the vertical major axis of length 10 and minor axis of length 8

Answer 1

(x/h)^2+(y/v)^2=1 where h is the horizontal radius and v is the vertical radius

In this question it seem that they are saying the length of the axis and not radius so I would cut them in half so that they are radii...then:

(x/4)^2+(y/5)^2=1

x^2/16+y^2/25=1

Answer 2

Answer: The required equation of the ellipse in standard form is
`(y^2)/(25)+(x^2)/(16)=1.`

Step-by-step explanation: We are given to find the equation of an ellipse in standard form with the vertical major axis of length 10 units and minor axis of length 8 units.

Since the major axis is vertical, so it will lie on the Y-axis. Let the standard form of the ellipse be given by

`(y^2)/(a^2)+(x^2)/(b^2)=1,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

where the length of major axis is 2a units and length of minor axis is 2b units.

According to the given information, we have

`2a=10\\\\\Rightarrow a=(10)/(2)\\\\\Rightarrow a=5`

and

`2b=8\\\\\Rightarrow b=(8)/(2)\\\\\Rightarrow b=4`

Substituting the values of a and b in equation (i), we get

`(y^2)/(5^2)+(x^2)/(4^2)=1\\\\\\\Rightarrow (y^2)/(25)+(x^2)/(16)=1.`

Thus, the required equation of the ellipse in standard form is
`(y^2)/(25)+(x^2)/(16)=1.`