Question

The equation of an ellipse is given by

Answer 1

Answer:

a). Image

b). $\frac{x^{2} }{a^{2}}+ \frac{y^{2} }{b^{2}}=1\\\frac{x^{2} }{3^{2}}+ \frac{y^{2} }{(\sqrt{6}) ^{2}}=1$

Step-by-step explanation:

a).

$\frac{x^{2}}{9}+ \frac{y^{2}}{6}=1\\ \frac{y^{2}}{6}=1-\frac{x^{2}}{9}\\y^{2} = 6- \frac{6x^{2}}{9}\\y=\sqrt{6}- \frac{\sqrt{2} }{\sqrt{3}}*x\\x=0\\y=\sqrt{6}$≅2.44

$x=3\\y=\sqrt{6}-\frac{\sqrt{2}}{\sqrt{3}} *3\\ y=2.44-2.44\\y=0$

Those points see in the image

(0,2.44) and (3, 0)

b).

$\frac{(x-h)^{2} }{a^{2}} +\frac{(y-k)^{2} }{b^{2}}=1\\(h,k)=(0,0) \\a=\sqrt{9} =3\\b=\sqrt{6} \\\frac{x^{2} }{3^{2} } +\frac{^{2} }{\sqrt{6} ^{2} }=1$