AP EAMCET · Maths · Application of Derivatives
If the lengths of the tangent, subtangent, normal and subnormal for the curve \(y=x^2+x-1\) at the point \((1,1)\) are \(a, b, c\) and \(d\) respectively, then their increasing order is
- A \(b, d, a, c\)
- B \(b, a, c, d\)
- C \(a, b, c, d\)
- D \(b, a, d, c\)
Answer & Solution
Correct Answer
(D) \(b, a, d, c\)
Step-by-step Solution
Detailed explanation
\(y' = 2x+1 \) \(m = y'(1) = 2(1)+1 = 3\) \(a = \left| \frac{y_0}{m} \sqrt{1+m^2} \right| = \left| \frac{1}{3} \sqrt{1+3^2} \right| = \frac{\sqrt{10}}{3} \approx 1.054 \) \(b = \left| \frac{y_0}{m} \right| = \left| \frac{1}{3} \right| = \frac{1}{3} \approx 0.333 \)…
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