The ellipse will be:

asked 2021-06-08

find the area of the largest rectangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

asked 2021-09-07

The plane \(\displaystyle{x}+{y}+{2}{z}={18}\) intersects the paraboloid \(\displaystyle{z}={x}^{{2}}+{y}^{{2}}\) in an ellipse. Find the points
on this ellipse that are nearest to and farthest from the origin.

asked 2021-09-03

Find the points on the ellipse \(\displaystyle{4}{x}^{{2}}+{y}^{{2}}={4}\) that are farthest away from the point (-1, 0).

(x, y) = ( ) (smaller y-value)

(x, y) = ( )(larger y-value)

(x, y) = ( ) (smaller y-value)

(x, y) = ( )(larger y-value)

asked 2021-05-03

Find the maximum volume of a rectangular box that is inscribed in a sphere of radius r.

asked 2021-05-25

Find the points on the ellipse \(4x^2 + y^2 = 4\) that are farthest away from the point (-1, 0).

(x, y) = ( ) (smaller y-value)

(x, y) = ( )(larger y-value)

(x, y) = ( ) (smaller y-value)

(x, y) = ( )(larger y-value)

asked 2021-05-08

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius .

asked 2021-09-07

Find the area of the surface.

The part of the paraboloid

\(\displaystyle{z}={1}−{x}^{{2}}−{y}^{{2}}\)

that lies above the plane

\(\displaystyle{z}=−{6}\)

The part of the paraboloid

\(\displaystyle{z}={1}−{x}^{{2}}−{y}^{{2}}\)

that lies above the plane

\(\displaystyle{z}=−{6}\)