AP EAMCET · Maths · Application of Derivatives
The number of points on the cure \(y=2 t^2+3 t-5\) and \(x=t^3-4 t^2-3 t\) such that the normals drawn at them on the curve are parallel to \(\mathrm{X}\) - axis is
- A 1
- B 4
- C 3
- D 2
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{\left(\frac{d y}{d t}\right)}{\left(\frac{d x}{d t}\right)}=\frac{4 t+3}{\left(3 t^2-8 t-3\right)}\) Hence slope of normal \(=-\frac{1}{\left(\frac{d y}{d x}\right)}\) \(=\frac{\left(3 t^2-8 t-3\right)}{(4 t+3)}\) Since slope of normal \(=\) Slope of…
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