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in Derivatives by (2.6k points)
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Find the equation of the tangent and the normal to the following curves at the indicated points: 

x = at2, y = 2at at t = 1.

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Best answer

finding slope of the tangent by differentiating x and y with respect to t

\(\frac{dx}{dt}=2at\)

\(\frac{dx}{dt}=2a\)

Now dividing \(\frac{dy}{dt}\) and \(\frac{dx}{dt}\) to obtain the slope of tangent

\(\frac{dy}{dx}=\frac{1}{t}\)

m(tangent) at t = 1 is 1

normal is perpendicular to tangent so, m1m2 = – 1

m(normal) at t = 1 is – 1

equation of tangent is given by y – y1 = m(tangent)(x – x1)

y – 2a = 1(x – a)

equation of normal is given by y – y1 = m(normal)(x – x1)

y – 2a = – 1(x – a)

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