Question

The foci of the ellipse 9x² + 25y² - 18x - 100y - 116 = 0 is

• A. (5,-2), (-3,2)
• B. (5,2)(-3,2)
• C. (5,2),(3,2)
• D. (-5,-2),(-3,2)

Answer 1

Answer: (B)

(5,2)(-3,2)

Answer 2

The given ellipse can put in the form of

$\frac{(x - 1)^{2}}{25} + \frac{(y - 2)^{2}}{9} = 1$

∴ e = $\sqrt{\frac{a^{2} - b^{2}}{a^{2}}}\mspace{6mu} = \mspace{6mu}\sqrt{\frac{25 - 9}{25}} = \frac{4}{5}$ foci = (α $\pm ae,\beta$)

where (α, β) = (1, 2) = centre = (5, 2), (-3, 2)