how do you find the equation of the tangent line at the given point on each curve?x2+ y2=25 , (-3,4)

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

x2+ y2=25 , (-3,4)

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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 = dy/dx

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 (x1,y1) is given by y - y1 = m(xx1)

Plugging the values,

Hence, the equation of the tangent line ...

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