TS EAMCET · Maths · Application of Derivatives
\(y=x^2\) is the given curve. Imagine that this curve is dragged along the positive \(\mathrm{X}\)-axis to a distance of ' \(a\) ' units. If the acute angle between the curves at two positions is \(\theta\) then
- A \(\theta=\frac{\pi}{2}\)
- B \(\tan \theta=\frac{2|a|}{\left|1-a^2\right|}\)
- C \(\cos \theta=\frac{2|a|}{\left|1-a^2\right|}\)
- D \(\theta=0\)
Answer & Solution
Correct Answer
(B) \(\tan \theta=\frac{2|a|}{\left|1-a^2\right|}\)
Step-by-step Solution
Detailed explanation
Given curve \(y=x^2\) and the another required curve is \(y=(x-a)^2\) Intersection point of two curves is \[ \begin{aligned} & x^2=(x-a)^2 \\ & x^2=x^2+a^2-2 a x \\ & a(a-2 x)=0 \\ & a=0, x=\frac{a}{2} \end{aligned} \] From \(y=x^2\) then, \[ \mathrm{y}=\frac{\mathrm{a}^2}{4} \]…
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