WBJEE · Maths · Properties of Triangles
Lines \(x+y=1\) and \(3 y=x+3\) intersect the ellipse \(x^{2}+9 y^{2}=9\) at the points \(P, Q\) and \(R\). The area of the \(\triangle P Q R\) is
- A \(\frac{36}{5}\)
- B \(\frac{18}{5}\)
- C \(\frac{9}{5}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{18}{5}\)
Step-by-step Solution
Detailed explanation
Given equation of ellipse \[ x^{2}+9 y^{2}=9 \] \(\Rightarrow \quad \frac{x^{2}}{9}+\frac{y^{2}}{1}=1\) and equation of lines \[ x+y=1 \text { and } 3 y=x+3 \] or \(\quad \frac{x}{(-3)}+\frac{y}{1}=1\) \(\therefore\) Area of…
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