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TS EAMCET · Maths · Ellipse

Equations of the latus rectum of the ellipse \(9 x^2+4 y^2-18 x-8 y-23=0\) are :

  1. A \(y= \pm \sqrt{5}\)
  2. B \(x= \pm \sqrt{5}\)
  3. C \(y=1 \pm \sqrt{5}\)
  4. D \(x=-1 \pm \sqrt{5}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(y=1 \pm \sqrt{5}\)

Step-by-step Solution

Detailed explanation

Equation of ellipse is \(9 x^2+4 y^2-18 x-8 y-23=0\) \(\Rightarrow \quad 9\left(x^2-2 x+1\right)-9+4\left(y^2-2 y+1\right)\) \(-4-23=0\) \(\Rightarrow \quad 9(x-1)^2+4(y-1)^2=36\) \(\Rightarrow \quad \frac{(x-1)^2}{4}+\frac{(y-1)^2}{9}=1\) Here \(\quad a < b\)…