Question

The lines $x+y=1$ and $3y=x+3$ intersect the ellipse $x^2+9y^2=9$ at the points $P,Q$ and $R$.

The area of the $△PQR$ is?

• A. $\frac{36}{5}$
• B. $\frac{18}{5}$
• C. $\frac{9}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is B $\frac{18}{5}$

Given equation of ellipse
$x^2+9y^2=9$
$\Rightarrow$ $\frac{x^2}{9}+\frac{y^2}{1}=1$
and equation of lines
$x+y=1$ and $3y=x+3$
$\frac{x}{(-3)}+\frac{y}{1}=1$
$\therefore$ Area of $△PQR=\left|\frac{1}{2}\left|\begin{array}{ccc}0& 1& 1\\ -3& 0& 1\\ 9/5& -4/5& 1\end{array}\right|\right|$
$=\frac{1}{2}\left|[\frac{24}{5}+\frac{12}{5}]\right|$
$=\frac{1}{2}\times \frac{36}{5}=\frac{18}{5}$