Write the equation of the ellipse that has its center at the origin, focus at (2,0) and vertex at (7,0)

Equation of ellipse:  (x/a)^2 + (y/b)^2 = 1,  where a and b are semi-major axes.

 

Here a = 7 from the fact that the vertex is at (7, 0) so a^2 = 49

 

There are two foci. One is given as (2, 0) so the other must be at (-2, 0).

 

The sum of the distance from one focus to the ellipse to the other focus is constant. Here it must be (7 - 2) + (7 + 2) → 14

 

The y vertex is at (0, b) so we must also have 2*sqrt(b^2 + 2^2) = 14

 

b^2 + 2^2 = 7^2. or b^^2 = 45

 

Hence we can write the ellipse equation as x^2/49 + y^2/45 = 1

 

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