Question

Asked May 8, 2019

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how do you find the equation of the tangent line at the given point on each curve?

x^{2}+ y^{2}=25 , (-3,4)

Step 1

To determine the equation of the tangent line, the slope of the curve at the given point is to be determined.

Slope of the curve is given by *m* = d*y*/d*x*

Applying derivative to the equation of the curve with respect to *x*:

Hence, the slope of the curve at (-3,4) is given by:

Step 2

The tangent line passes through the given point.

Equation of a line with slope *m* and passing through the point (*x*1,*y*1) is given by *y *- *y*1 = *m*(*x* – *x*1)

Plugging the values,

Hence, the equation of the tangent line ...

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