how do you find the equation of the tangent line at the given point on each curve?
x2+ y2=25 , (-3,4)
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:
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(x – x1)
Plugging the values,
Hence, the equation of the tangent line ...
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