COMEDK · Maths · 27. Application of Derivatives
If tangent to the curve \(x=a t^{2}, y=2 a t\) is perpendicular to \(X\)-axis, then its point of contact is
- A \((a, a)\)
- B \((0, a)\)
- C \((0,0)\)
- D \((a, 0)\)
Answer & Solution
Correct Answer
(C) \((0,0)\)
Step-by-step Solution
Detailed explanation
We have, \[ x=a t^{2}, y=2 a t \] Now, \(\quad \frac{d x}{d t}=2 a t, \frac{d y}{d t}=2 a\) \[ \therefore \quad \frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{2 a}{2 a t}=\frac{1}{t} \] Since, tangent is perpendicular to \(X\)-axis, then \(\frac{d y}{d x}=\frac{1}{0}\)…
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