Mathematics

Mathematics

Problem

Let the curve be defined by

x^{2}+xy+y^{2}=7

and consider the point

R(1,2)

. a. Confirm that

R

lies on the curve. b. Compute

\dfrac{dy}{dx}

at

R

. c. Express the tangent line at

R

in parametric form with parameter

t

, choosing

t=0

to correspond to the point

R

. Provide both

x(t)

and

y(t)

. (For example, you may write

x(t)=\ldots

and

y(t)=\ldots

.)

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