WBJEE · Maths · Parabola
Consider the parabola \(y^{2}=4 x\). Let \(P\) and \(Q\) be points on the parabola where \(P(4,-4)\) and \(Q (9,6)\). Let \(R\) be a point on the arc of the parabola between \(P\) and \(Q\). Then, the area of \(\Delta P Q R\) is largest when
- A \(\angle P Q A=90^{\circ}\)
- B \(R(4,4)\)
- C \(R\left(\frac{1}{4}, 1\right)\)
- D \(R\left(1, \frac{1}{4}\right)\)
Answer & Solution
Correct Answer
(C) \(R\left(\frac{1}{4}, 1\right)\)
Step-by-step Solution
Detailed explanation
Let \(\quad f(x)=x \log x+x-3\) \(\Rightarrow \quad f^{\prime}(x)=x \cdot \frac{1}{x}+\log x+1\) \(\Rightarrow \quad f^{\prime}(x)=\log x+2>0\) \(\Rightarrow f(1)=-2\) and \(f(3)=3 \log 3, f(1) \cdot f(3 0\) Equation of \(P Q\) is \(2 x-y=12\) Perpendicular distance…
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