WBJEE · Maths · Application of Derivatives
The chord of the curve \(y=x^{2}+2 a x+b\) joining the points where \(x=\alpha\) and \(x=\beta,\) is parallel to the tangent to the curve at abscissa \(x\) is equal to
- A \(\frac{a+b}{2}\)
- B \(\frac{2 a+b}{3}\)
- C \(\frac{2 \alpha+\beta}{3}\)
- D \(\frac{\alpha+\beta}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\alpha+\beta}{2}\)
Step-by-step Solution
Detailed explanation
Given curve, At \(y=x^{2}+2 a x+b\) \(x=a\) \(y=\alpha^{2}+2 a \alpha+b\) and at \(x=\beta\) \(y=\beta^{2}+2 a \beta+b\) \(\therefore\) Slope of line joining \(\left(\alpha, \alpha^{2}+2 a \alpha+b\right)\) and \(\left(\beta, \beta^{2}+2 a \beta+b\right)\) is…
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