Question

What are the foci of the ellipse given by the equation 100x2 + 64y2 = 6,400?

Answer 1

Quadratic relations and comic sections unit test part 1

11. a. (0, +/- 6)

Answer 2

The ordinary equation of a ellipse is given as follows:


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

Being:

a: Semi-major axis
b: Semi-minor axis

Our equation is:


`100 x^(2) + 64y^(2) = 6400`

Multiplying this equation by:


`(1)/((100)(64))`

Then:


`( x^(2))/(64) + (y^(2))/(100) = 1`

We can see that:


`a = √(100) = 10`

`b = √(64) = 8`

Then the semi-major axis is on the y-axis, and the focus are located there, so:


`F_(1) = (0,c)`

`F_(2) = (0,-c)`

We also know that the relation between a, b and c is:


`c^(2) = a^(2) - b^(2)`

`c^(2) = 100 - 64 = 36`

`c = √(36) = 6`

Then, the focus are:


`F_(1)(0,6)`

`F_(1)(0,-6)`