Find an equation for the ellipse that satisfies the given conditions. Endpoints of major axis: (±7, 0), distance between foci: 4

Answer 1

Equation of ellypse x²/a² + y²/b² = 1. Now a = 7; 2c = 4, c = 2. Then b² = a² - c² = 49 - 4 = 45.

Equation of ellypse: x²/49 - y²/45 = 1

Answer 2

hi,

when you have information such as major axis: (±7, 0),

the best way is coordinate plane.

Now you see major axis lies on the x-axis, so you figure out :

1) it is horizontal ellipse

2) the mid point of major axis is origin that it is center of ellipse (0,0)

3) you know 2a = 14 or a = 7

4) the equation of ellipse is x^2/a^2 + y^2/b^2 =1

let us follow given information  foci: 4

now you Know 2c=4 --> c = 2

only you need to fine b

a^ = b^2 + c^2 ----> 7^2 = b^2 + 2^2 ----> b^2 = 45

Now, it is enough to replace all information to the equation

x^2 / 49 + y^2/45 = 1

I hope it is useful in order to find the best method for solving,

Minoo