Question

The equation of the latusrecta of the ellipse $9x^2+4^2-18x-8y-23=0$ are

• A. $y=\pm \sqrt{5}$
• B. $x=\pm \sqrt{5}$
• C. $y=1\pm \sqrt{5}$
• D. $x=1\pm \sqrt{5}$

Answer 1

Answer: (C)

$y=1\pm \sqrt{5}$

equation of ellipse is ${9x}^2+{4y}^2-18x-8y-23=0$

$\Rightarrow (9x^2-18x+9)+(4y^2-8y+4)-23-9-4=0$

$\Rightarrow 9(x-1{)}^2+4(y-1{)}^2=36$

$\Rightarrow \frac{(x-1{)}^2}{4}+\frac{(y-1{)}^2}{9}=1$

So, equation of latus recta is $(y-1)=\pm be$

$y=1\pm \sqrt{b^2-a^2}\Rightarrow y=1\pm \sqrt{5}$