AP EAMCET · Maths · Application of Derivatives
If \(T\) is the length of the subtangent drawn at any point on the curve \(3 y^2=4 x^3\) and \(N\) is the length of the subnormal at the same point, then \((\beta T)^2=\)
- A \(4 N^2\)
- B \(4 \mathrm{~N}\)
- C \(2 \mathrm{~N}\)
- D \(8 \mathrm{~N}^2\)
Answer & Solution
Correct Answer
(C) \(2 \mathrm{~N}\)
Step-by-step Solution
Detailed explanation
The equation of given curve is \(3 y^2=4 x^3\) ...(i) Let a point \(P(h, k)\) on the curve (i), so \(\left.\frac{d y}{d x}\right|_{(h, k)}=\frac{2 h^2}{k}\) Now, length of sub-tangent, \(T=\left|k \frac{k}{2 h^2}\right|=\frac{1}{2} \frac{k^2}{h^2}\) and length of sub-normal,…
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