Find an equation of the form ax2 + by2 = c for the ellipse that passes through the given points. (2, 5) and (6, 3)

Answer 1

One approach to this problem is to note that the given equation is similar to a textbook ellipse form if c =1

So: Search for an equation of the form a x² + b y² = 1

Substituting in the points, gives two equations with two unknowns (a and b) with the solution

a = 1/54 and b = 1/27

So: x² /54 + y² / 27 = 1

Thus the semi-major axis is sqrt(54) and the semi-minor axis is sqrt( 27)