Question

The foci of the conic section

25x² + 16y² –150 x = 175 are

• A. (0, ± 3)
• B. (0, ±2)
• C. (3, ±3)
• D. (0, ±1)

Answer 1

Answer: (C)

(3, ±3)

Answer 2

$\frac{(x - 3)^{2}}{16}$+$\frac{y^{2}}{25}$= 1

Here (a < b); centre C (3, 0)

e = $\sqrt{1 - \frac{a^{2}}{b^{2}}}$= $\sqrt{1 - \frac{16}{25}}$= $\frac{3}{5}$

\ focus ̃ CS = be = 5 $\left( \frac{3}{5} \right)$= 3

̃ S(3, y₁) = (3, 0 + be) = (3, 3)

S¢(3, y₂) = (3, 0 – be) = (3, –3)

̃ S & S¢ = (3, ± 3)