To find: The equation of the tangent line to the given equation at the point.
The equation of the tangent line to the equation at the point is .
The curve is .
The point is .
Derivative rules: Chain rule
If and are both differentiable functions, then .
The equation of the tangent line at is, (1)
Where, m is the slope of the tangent line at and .
Consider the equation .
Differentiate the given equation implicitly with respect to x,
Apply the chain rule and simplify the terms,
Separate to one side of the equation,
Therefore, the derivative of the equation is .
The slope of the tangent line at the point is computed as follows,
Thus, the slope of the tangent line at is .
Substitute for and in equation (1),
Therefore, the equation of the tangent line to the equation at the point is .
The graph of the curve and the tangent line is shown below in Figure 1.
From Figure 1, it is observed that the line is tangent to the curve at the point .
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