JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the line \(y =4+ kx , k >0\), is the tangent to the parabola \(y = x - x ^{2}\) at the point \(P\) and \(V\) is the vertex of the parabola, then the slope of the line through \(P\) and \(V\) is
- A \(\frac{3}{2}\)
- B \(\frac{26}{9}\)
- C \(\frac{5}{2}\)
- D \(\frac{23}{6}\)
Answer & Solution
Correct Answer
(C) \(\frac{5}{2}\)
Step-by-step Solution
Detailed explanation
Slope of tangent at \(P =\) Slope of line \(AP\) \(\left. y ^{\prime}\right|_{ P }=1-2 \alpha=\frac{\alpha-\alpha^{2}-4}{\alpha}\) Solving \(\alpha=-2 \Rightarrow P(-2,-6)\) Slope of \(PV =\frac{5}{2}\)
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