JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let PQ be a focal chord of the parabola \(y^2=36 x\) of length \(100\), making an acute angle with the positive \(x\)-axis. Let the ordinate of \(P\) be positive and \(M\) be the point on the line segment \(P Q\) such that \(P M: M Q=3: 1\). Then which of the following points does NOT lie on the line passing through \(M\) and perpendicular to the line \(PQ\) ?
- A \((-3,43)\)
- B \((-6,45)\)
- C \((3,33)\)
- D \((6,29)\)
Answer & Solution
Correct Answer
(A) \((-3,43)\)
Step-by-step Solution
Detailed explanation
\(9\left(t+\frac{1}{t}\right)^2=100\) \(t=3\) \(\Rightarrow P(81,54) \quad Q(1,-6)\) \(M(21,9)\) \(\Rightarrow L \text { is }(y-9)=\frac{-4}{3}(x-21)\) \(3 y-27=-4 x+84\) \(4 x+3 y=111\)
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