AP EAMCET · Maths · Application of Derivatives
If the points of contact of the tangents drawn from \((0,0)\) to the curve \(y=x^2+3 x+4\) are \((\alpha, \beta)\) and \((\gamma, \delta)\), then \(\beta+\delta=\)
- A \(7\)
- B \(25\)
- C \(16\)
- D \(13\)
Answer & Solution
Correct Answer
(C) \(16\)
Step-by-step Solution
Detailed explanation
Given \(y=x^2+3 x+4\) Now \(\frac{d y}{d x}=2 x+3\) At \((h, k)\) \(\left.\Rightarrow \frac{d y}{d x}\right|_{(h, k)}=2 h+3\) So, equation of tangent at (h, k) \(y-k=(2 h+3)(x-h)\) It is passes through \((0,0)\) So \(-k=(2 h+3)(-h) \Rightarrow k=2 h^2+3 k...(i)\) and…
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