Conic Sections - Ellipses

$$\frac{x^2}{25}+\frac{y^2}{16}=1$$

$$\frac{x^2}{16}+\frac{y^2}{25}=1$$

$$\frac{\left(x-1\right)^2}{9}+\frac{\left(y-5\right)^2}{25}=1$$

Given $$16x^2+25y^2-32x+50y+16=0$$

a=​ (a)  

b=​ (b)  

Find an equation of an ellipse with its center at the origin.

vertices: $$\left(\pm5,0\right)$$

foci: $$\left(\pm2,0\right)$$

Find an equation of an ellipse with its center at the origin.

focus: $$\left(\pm5,0\right)$$

major axis length: $$12$$

Find the equation of the ellipse in standard form.

vertices: $$\left(0,2\right),\ \left(4,2\right)$$

minor axis length: $$2$$

Find the equation of the ellipse in standard form.

vertices: $$\left(3,1\right),\ \left(3,9\right)$$

minor axis length: $$6$$

Find the equation of the ellipse in standard form.

vertices: $$\left(5,0\right),\ \left(5,12\right)$$

endpoints of minor axis: $$\left(0,6\right),\ \left(10,6\right)$$

Write an equation for the ellipse with each set of characteristics. Vertices ( 4, 3), (4, - 9). Length of minor axis is 8