8.1 The ellipse  (Page 9/16)

$\frac{{\left(x-2\right)}^2}{7^2}+\frac{{\left(y-4\right)}^2}{5^2}=1;$ Endpoints of major axis $\left(9,4\right),\left(-5,4\right).$ Endpoints of minor axis $\left(2,9\right),\left(2,-1\right).$ Foci at $\left(2+2\sqrt{6},4\right),\left(2-2\sqrt{6},4\right).$

$\frac{{\left(x+5\right)}^2}{2^2}+\frac{{\left(y-7\right)}^2}{3^2}=1;$ Endpoints of major axis $\left(-5,10\right),\left(-5,4\right).$ Endpoints of minor axis $\left(-3,7\right),\left(-7,7\right).$ Foci at $\left(-5,7+\sqrt{5}\right),\left(-5,7-\sqrt{5}\right).$

$\frac{{\left(x-1\right)}^2}{3^2}+\frac{{\left(y-4\right)}^2}{2^2}=1;$ Endpoints of major axis $\left(4,4\right),\left(-2,4\right).$ Endpoints of minor axis $\left(1,6\right),\left(1,2\right).$ Foci at $\left(1+\sqrt{5},4\right),\left(1-\sqrt{5},4\right).$

$\frac{{\left(x-3\right)}^2}{{\left(3\sqrt{2}\right)}^2}+\frac{{\left(y-5\right)}^2}{{\left(\sqrt{2}\right)}^2}=1;$ Endpoints of major axis $\left(3+3\sqrt{2},5\right),\left(3-3\sqrt{2},5\right).$ Endpoints of minor axis $\left(3,5+\sqrt{2}\right),\left(3,5-\sqrt{2}\right).$ Foci at $\left(7,5\right),\left(-1,5\right).$

$\frac{{\left(x+5\right)}^2}{{\left(5\right)}^2}+\frac{{\left(y-2\right)}^2}{{\left(2\right)}^2}=1;$ Endpoints of major axis $\left(0,2\right),\left(-10,2\right).$ Endpoints of minor axis $\left(-5,4\right),\left(-5,0\right).$ Foci at $\left(-5+\sqrt{21},2\right),\left(-5-\sqrt{21},2\right).$

$\frac{{\left(x+3\right)}^2}{{\left(5\right)}^2}+\frac{{\left(y+4\right)}^2}{{\left(2\right)}^2}=1;$ Endpoints of major axis $\left(2,-4\right),\left(-8,-4\right).$ Endpoints of minor axis $\left(-3,-2\right),\left(-3,-6\right).$ Foci at $\left(-3+\sqrt{21},-4\right),\left(-3-\sqrt{21},-4\right).$

Foci $\left(-3,-1+\sqrt{11}\right),\left(-3,-1-\sqrt{11}\right)$

Focus $\left(0,0\right)$

Foci $\left(-10,30\right),\left(-10,-30\right)$

Center $\left(0,0\right),$ Vertices $\left(4,0\right),\left(-4,0\right),(0,3),(0,-3),$ Foci $\left(\sqrt{7},0\right),\left(-\sqrt{7},0\right)$

Center $\left(0,0\right),$ Vertices $\left(\frac{1}{9},0\right),\left(-\frac{1}{9},0\right),\left(0,\frac{1}{7}\right),\left(0,-\frac{1}{7}\right),$ Foci $\left(0,\frac{4\sqrt{2}}{63}\right),\left(0,-\frac{4\sqrt{2}}{63}\right)$

Center $\left(-3,3\right),$ Vertices $\left(0,3\right),\left(-6,3\right),\left(-3,0\right),\left(-3,6\right),$ Focus $\left(-3,3\right)$

Note that this ellipse is a circle. The circle has only one focus, which coincides with the center.

Center $\left(1,1\right),$ Vertices $\left(5,1\right),\left(-3,1\right),\left(1,3\right),\left(1,-1\right),$ Foci $\left(1,1+4\sqrt{3}\right),\left(1,1-4\sqrt{3}\right)$

Center $\left(-4,5\right),$ Vertices $\left(-2,5\right),\left(-6,4\right),\left(-4,6\right),\left(-4,4\right),$ Foci $\left(-4+\sqrt{3},5\right),\left(-4-\sqrt{3},5\right)$

Center $\left(-2,1\right),$ Vertices $\left(0,1\right),\left(-4,1\right),\left(-2,5\right),\left(-2,-3\right),$ Foci $\left(-2,1+2\sqrt{3}\right),\left(-2,1-2\sqrt{3}\right)$

Center $\left(-2,-2\right),$ Vertices $\left(0,-2\right),\left(-4,-2\right),\left(-2,0\right),\left(-2,-4\right),$ Focus $\left(-2,-2\right)$

$\frac{x^2}{25}+\frac{y^2}{29}=1$

$\frac{{\left(x-4\right)}^2}{25}+\frac{{\left(y-2\right)}^2}{1}=1$

$\frac{{\left(x+3\right)}^2}{16}+\frac{{\left(y-4\right)}^2}{4}=1$

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

$\frac{{\left(x+2\right)}^2}{4}+\frac{{\left(y-2\right)}^2}{9}=1$

$\text{Area = 12π}\text{square}\text{units}$

$\text{Area = 2}\sqrt{\text{5}}\text{π}\text{square}\text{units}$

$\text{Area = 9π}\text{square}\text{units}$

$\frac{x^2}{4h^2}+\frac{y^2}{\frac{1}{4}{h}^2}=1$

$\frac{x^2}{400}+\frac{y^2}{144}=1$ . Distance = 17.32 feet

Approximately 51.96 feet