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JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(\ell\) be a line which is normal to the curve \(y=2 x^{2}+x+2\) at a point \(P\) on the curve. If the point \(Q(6,4)\) lies on the line \(\ell\) and \(O\) is origin, then the area of the triangle \(OPQ\) is equal to.......
- A \(13\)
- B \(83\)
- C \(130\)
- D \(10\)
Answer & Solution
Correct Answer
(A) \(13\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=4 x+1\) Let \(P\) be \((h, k)\), then normal at \(P\) is \(y-k=-\frac{1}{4 h+1}(x-h)\) This passes through \(Q (6,4)\) \(\therefore 4- k =-\frac{1}{4 h +1}(6- h )\) \(\Rightarrow(4 h +1)(4- k )+6- h =0\) Also \(k =2 h ^{2}+ h +2\)…
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