7.3 Ellipses practice 2

Write the center,foci, and vertices of the ellipse [math]9y^2+36y+25x^2-50x-164=0[/math].

Write an equation for the ellipse

Write an equation for the ellipse:

Find the standard form of the equation of the ellipse centered at [math](2,-1)[/math] with a vertex [math]\left(2,\dfrac{1}{2}\right)[/math] and a minor axis of length 2.

Find the standard form of the equation of the ellipse with foci at [math](0,0)[/math] and [math](4,0)[/math] and a major axis of length 8.

(Calculator) The opening of a tunnel is in the shape of the upper half of an ellipse 152 feet wide and 38 feet high. Find the height, in feet, of the arch 19 feet from the center of the tunnel.

The perimeter of a triangle with one vertex on the ellipse [math]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/math] and the other two vertices at the foci of the ellipse would be

Find the center of the ellipse: [math]x^2+2y^2-4x-16y+32=0[/math]

Find the vertices of the ellipse: [math]\dfrac{(x+\frac{1}{2})^2}{8}+\dfrac{(y-\frac{1}{2})^2}{4}=1[/math]

Find the standard form of the equation of the ellipse with foci [math](-\sqrt{11},5)[/math] and [math](\sqrt{11},5)[/math] and a vertex [math](6,5)[/math]

(Calculator) A carpenter wishes to construct an elliptical table top form a 4ft by 8ft sheet of plywood. He will trace out the ellipse using the “thumbtack and string” method. What length of string should be use, and how far apart should the tacks be located, if the ellipse is to be the largest possible that can be cut of the plywood sheet?