JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the tangent of the curve, \(y=e^{x}\) at a point \(\left( c , e ^{ c }\right)\) and the normal to the parabola, \(y ^{2}=4 x\) at the point \((1,2)\) intersect at the same point on the \(x\)-axis, then the value of \(c\) is
- A \(3\)
- B \(4\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(4\)
Step-by-step Solution
Detailed explanation
\(y=e^{x} \Rightarrow \frac{d y}{d x}=e^{x}\) \(m =\left(\frac{ dy }{ dx }\right)_{\left( c , e ^{ e }\right)}= e ^{ c }\) \(\Rightarrow \quad\) Tangent at \(\left( c , e ^{ c }\right)\) \(y-e^{c}=e^{c}(x-c)\) it intersect x-axis Put \(\quad y =0 \Rightarrow x = c -1\)…
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