AP EAMCET · Maths · Application of Derivatives
If the equation of tangent at \((2,3)\) on \(y^2=a x^3+b\) is \(y=4 x-5\), then the value of \(a^2+b^2=\)
- A 51
- B 53
- C 28
- D 25
Answer & Solution
Correct Answer
(B) 53
Step-by-step Solution
Detailed explanation
Given the curve, \(y^2=a x^3+b\) \(\Rightarrow 2 y \frac{d y}{d x}=3 a x^2 \Rightarrow \frac{d y}{d x}=\frac{3 a x^2}{2 y}\) at \((2,3)\), \(\frac{d y}{d x}=\frac{12 a}{6}=2 a\) Since, slope of tangent to the line \(y=4 x-5\) is 4…
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