Answer:
The directrix of the ellipse is:
x= -3.25 and x=9.25
Step-by-step explanation:
As we know that for any ellipse equation of the type:
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex] and a>b
The directrix is given by:
[tex]x=h\pm \dfrac{a}{e}[/tex]
where,
[tex]e=\sqrt{1-\dfrac{b^2}{a^2}}[/tex]
Here we have the equation of parabola as:
[tex]\dfrac{(x-3)^2}{5^2}+\dfrac{(y-2)^2}{3^2}}=1[/tex]
Hence, we have:
[tex]h=3,\ k=2,\ a=5,\ b=3\\\\and\\\\e=\sqrt{1-\dfrac{3^2}{5^2}}\\\\e=\sqrt{1-\dfrac{9}{25}}\\\\e=\sqrt{\dfrac{25-9}{25}}\\\\\\e=\sqrt{\dfrac{16}{25}}\\\\e=\dfrac{4}{5}[/tex]
Hence, we have: the directrix as:
[tex]x=3\pm \dfrac{5}{\dfrac{4}{5}}\\\\\\x=3\pm \dfrac{25}{4}\\\\Hence, x=9.25\ and\ x=-3.25[/tex]
Hence, the equation of directrix is:
x= -3.25 and x=9.25
