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JEE Mains · Maths · STD 12 - 6. Application of derivatives
If \(P\) is a point on the parabola \(y=x^{2}+4\) which is closest to the straight line \(y =4 x -1,\) then the co-ordinates of \(P\) are :
- A \((3,13)\)
- B \((1,5)\)
- C \((-2,8)\)
- D \((2,8)\)
Answer & Solution
Correct Answer
(D) \((2,8)\)
Step-by-step Solution
Detailed explanation
\(P: y=x^{2}+4\) \(k=h^{2}+4\) \(L : y =4 x -1\) \(y-4 x+1=0\) \(d = AB =\left|\frac{ k -4 h +1}{\sqrt{5}}\right|=\left|\frac{ h ^{2}-4-4 h +1}{\sqrt{5}}\right|\) \(\frac{ d ( d )}{ dh }=\frac{2 h -4}{\sqrt{5}}=0\) \(h =2\)…
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