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NDA 2025 Maths · Mathematics · Derivatives · medium

For the parabola given parametrically by x=at^2, y=2at, the slope of the tangent at the point with parameter t=2 is

Single correct option

For the parabola given parametrically by x=at2x=at^2, y=2aty=2at, the slope of the tangent at the point with parameter t=2t=2 is
  1. A. 22
  2. B. 12\dfrac12
  3. C. 4a4a
  4. D. 14a\dfrac1{4a}
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Answer: (B) 12\dfrac12

dydt=2a\frac{dy}{dt}=2a and dxdt=2at\frac{dx}{dt}=2at, so dydx=1t\frac{dy}{dx}=\frac1t, which is 12\frac12 at t=2t=2. The constant aa cancels, which rules out the options containing aa. The value 22 inverts the slope. This is the slope at the parameter tt on the parabola y2=4axy^2=4ax.
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