Find the standard form of the equation of the ellipse satisfying the given conditions below. Endpoints of major axis: (-11, 1) and (7, 1); endpoints of minor axis: (-2, -2) and (-2, 4)

Solution:

The information regarding the ellipse is summarised in the diagram below:

The value of a = 9 (Half of the length of the major axis which is 2a = 18)

And The value of b = 3 (half of the length of the minor axis which is 2b = 6)

The the standard form of equation of the ellipse is given by:

\(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1\)

Since a = 9 and b = 3, the equation for the ellipse is:

\(\frac{x^{2}}{9^{2}} + \frac{y^{2}}{3^{2}} = 1\)

\(\frac{x^{2}}{81} + \frac{y^{2}}{9} = 1\)

Find the standard form of the equation of the ellipse satisfying the given conditions below. Endpoints of major axis: (-11, 1) and (7, 1); endpoints of minor axis: (-2, -2) and (-2, 4)

Summary:

The standard form of the equation of the ellipse with endpoints of major axis: (-11, 1) and (7, 1); endpoints of minor axis: (-2, -2) and (-2, 4) is \(\frac{x^{2}}{81} + \frac{y^{2}}{9} = 1\)