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AP EAMCET · Maths · Parabola

The length of the latus rectum of \(9 x^2+25 y^2-90 x-150 y+225=0\) is

  1. A \(\frac{50}{3}\)
  2. B \(\frac{18}{5}\)
  3. C \(\frac{18}{25}\)
  4. D \(\frac{9}{25}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{18}{5}\)

Step-by-step Solution

Detailed explanation

\(9 x^2+25 y^2-90 x-150 y+225=0\) \(9(x-5)^2 + 25(y-3)^2 = 225\) \(\frac{(x-5)^2}{25} + \frac{(y-3)^2}{9} = 1\) \(a^2=25, b^2=9 \implies a=5, b=3\) Latus Rectum \(= \frac{2b^2}{a} = \frac{2(9)}{5} = \frac{18}{5}\)