Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
The equation of ellipse of the given figure is :
[tex]\dfrac{(x-3)^2}{25}+\dfrac{(y-2)^2}{9}=1[/tex]
So, the major axis = 5 units = a
minor axis = 3 units = b
So, the formula for directrices would be
[tex]x=h\pm \dfrac{a^2}{c}\\\\here,\ c=\sqrt{a^2-b^2}\\\\c=\sqrt{25-9}\\\\c=\sqrt{16}\\\\c=4\\\\x=3+\dfrac{25}{4}\\\\x=9.25\\\\and\\x=3-\dfrac{25}{4}\\\\x=-3.25[/tex]
Hence, the directrices of the ellipse would be
x = 9.25 and x = -3.25
Thus, Second option is correct.
