Answer:
a). Image
b). [tex]\frac{x^{2} }{a^{2}}+ \frac{y^{2} }{b^{2}}=1\\\frac{x^{2} }{3^{2}}+ \frac{y^{2} }{(\sqrt{6}) ^{2}}=1[/tex]
Step-by-step explanation:
a).
[tex]\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}[/tex]≅2.44
[tex]x=3\\y=\sqrt{6}-\frac{\sqrt{2}}{\sqrt{3}} *3\\ y=2.44-2.44\\y=0[/tex]
Those points see in the image
(0,2.44) and (3, 0)
b).
[tex]\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[/tex]
