Q98 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

If $m$ is the length of the latus rectum and $n$ is the length of the major axis of the ellipse $25 x^2+16 y^2-150 x-64 y-111=0$, then the ordered pair $(m, n)=$

  • A
    $\left(\frac{16}{5}, 10\right)$
  • Correct answer
    B
    $\left(\frac{32}{5}, 10\right)$
  • C
    $\left(\frac{25}{2}, 8\right)$
  • D
    $\left(\frac{25}{4}, 8\right)$

Solution

Given equation of ellipse is $25 \mathrm{x}^2+16 \mathrm{y}^2-150 \mathrm{x}-$ $64 \mathrm{y}-111=0$ On arranging it we get, $$ \begin{aligned} & \frac{(\mathrm{x}-3)^2}{4^2}+\frac{(\mathrm{y}-2)^2}{5^2}=1 \\ & \Rightarrow \mathrm{a}=4, \text { and } \mathrm{b}=5 \\ & \text { now } \eta=\frac{2 \mathrm{a}^2}{\mathrm{~b}}=\frac{2 \times 16}{5}=\frac{32}{5} \\ & \mathrm{~m}=2 \mathrm{~b}=2 \times 5=10 \\ & \text { Hence }(\mathrm{n}, \mathrm{m}) \equiv\left(\frac{32}{5}, 10\right) \end{aligned} $$

Hence, the correct answer is option: 'B'.

Relevant Questions