JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the ellipse \(E : x ^2+9 y ^2=9\) intersect the positive \(x\) - and \(y\)-axes at the points \(A\) and \(B\) respectively Let the major axis of \(E\) be a diameter of the circle \(C\). Let the line passing through \(A\) and \(B\) meet the circle \(C\) at the point \(P\). If the area of the triangle which vertices \(A, P\) and the origin \(O\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(m - n\) is equal to
- A \(18\)
- B \(16\)
- C \(17\)
- D \(15\)
Answer & Solution
Correct Answer
(C) \(17\)
Step-by-step Solution
Detailed explanation
For line \(AB x+3 y =3\) and circle is \(x ^2+ y ^2=9\) \((3-3 y)^2+y^2=9\) \(\Rightarrow 10 y^2-18 y=0\) \(\Rightarrow y=0, \frac{9}{5}\) \(\therefore \text { Area }=\frac{1}{2} \times 3 \times \frac{9}{5}=\frac{27}{10}\) \(m - n =17\)
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