Question

I need help on two questions!

1. Write the equation of an ellipse with vertices (10, 0) and (-10, 0) and co-vertices (0, 2) and (0, -2).

second question in below.

Answer 1

1) Answer:
`(x^(2))/(100) +(y^(2))/(4) = 1`

Step-by-step explanation:

The equation of an ellipse is:
`((x-h)^(2))/(a^(2)) +((y-k)^(2))/(b^(2)) = 1` ; where (h, k) is the center, "a" is the x-radius, and "b" is the y-radius.

Center Radius

x-axis: (10 + -10)/2 = 0 10 - 0 = 10

• h = 0 a = 10

y-axis: (2 + -2)/2 = 0 2 - 0 = 2

• k = 0 b = 2

Now, input the values into the equation:

`((x-0)^(2))/(10^(2)) +((y-0)^(2))/(2^(2)) = 1`

`(x^(2))/(100) +(y^(2))/(4) = 1`

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2) Answer:
`(x^(2))/(1) +((y+2)^(2))/(4) = 1`

Step-by-step explanation:

Vertices are: (0, 1) and (0, -5) ------> x-values are the same, y = 1, -5

Covertices are: (-1, -2) and (1, -2) ----> y-values are the same, x = -1, 1

Center Radius

x-axis: (-1 + 1)/2 = 0 1 - 0 = 1

• h = 0 a = 1

y-axis: (1 + -5)/2 = -2 1 - (-2) = 3

• k = -2 b = 3

Now, input the values into the equation:

`((x-h)^(2))/(a^(2)) +((y-k)^(2))/(b^(2)) = 1`

`((x-0)^(2))/(1^(2)) +((y-(-2))^(2))/(3^(2)) = 1`

`(x^(2))/(1) +((y+2)^(2))/(9) = 1`