MATH SOLVE

5 months ago

Q:
# WILL GIVEBRAINLIEST AND 25 PTS PLEASE HURRY!!!Which lines are the directrices of the ellipse?x = −4.25 and x = 8.25 x = −3.25 and x = 9.25y = −4.25 and y = 8.25 y = −3.25 and y = 9.25

Accepted Solution

A:

Answer:The directrix of the ellipse is:x= -3.25 and x=9.25Step-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>bThe 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