AP EAMCET · Maths · Application of Derivatives
The points on the curve \(y^2=x+\sin x\) at which the normal is parallel to the Y-axis lie on
- A a line parallel to \(Y\)-axis
- B a circle with centre at origin
- C a parabola
- D a pair of lines bisecting the angle between the coordinate axes
Answer & Solution
Correct Answer
(C) a parabola
Step-by-step Solution
Detailed explanation
The given curve is \(y^2=x+\sin x\) ...(i) \(\Rightarrow \frac{d y}{d x}=\frac{1+\cos x}{2 y}\) Now, slope of the normal is \(m=-\frac{1}{\left(\frac{d y}{d x}\right)}=-\frac{2 y}{1+\cos x}\) \(\therefore \quad\) Normal is parallel to \(y\)-axis…
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