Question:
If \(x=at^2,\ y=2at\), find the value of \(\dfrac{dy}{dx}\).
If \(x=at^2,\ y=2at\), find the value of \(\dfrac{dy}{dx}\).
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Differentiate both x and y with respect to t, then divide.
Updated On: Sep 23, 2026
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Solution and Explanation
Step 1: Differentiating parametrically:
\(\dfrac{dx}{dt}=2at\) and \(\dfrac{dy}{dt}=2a\).
Step 2: Applying the chain rule:
\(\dfrac{dy}{dx}=\dfrac{dy/dt}{dx/dt}=\dfrac{2a}{2at}\).
Final Answer:
\[ \boxed{\dfrac{dy}{dx}=\dfrac{1}{t}} \]
\(\dfrac{dx}{dt}=2at\) and \(\dfrac{dy}{dt}=2a\).
Step 2: Applying the chain rule:
\(\dfrac{dy}{dx}=\dfrac{dy/dt}{dx/dt}=\dfrac{2a}{2at}\).
Final Answer:
\[ \boxed{\dfrac{dy}{dx}=\dfrac{1}{t}} \]
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