JEE Mains · Maths · STD 12 - 6. Application of derivatives
The shortest distance between the line \(y = x\) and the curve \(y^2 = x - 2\) is
- A \(\frac{{11}}{{4\sqrt 2 }}\)
- B \(2\)
- C \(\frac{{7}}{{4\sqrt 2 }}\)
- D \(\frac{7}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{{7}}{{4\sqrt 2 }}\)
Step-by-step Solution
Detailed explanation
We have \({\left. {2y\frac{{dy}}{{dx}} = 1 \Rightarrow \frac{{dy}}{{dx}}} \right]_{p\left( {2 + {t^2},t} \right)}}\) \( = \frac{1}{{2t}} = 1\) \(\Rightarrow \quad t=\frac{1}{2}\) \(\therefore \) \(\quad P\left(\frac{9}{4}, \frac{1}{2}\right)\) So, shortest distance…
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