Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). an equation of the tangent line to the lemniscate at the given point is

The equation of the tangent line to the curve is expressed as

The formula for calculating the equation of a line in point-slope form is expressed as y-y0 = m(x-x0)

m is the slope

(x0, y0) is the point on the line

Given the equation

To get the required slope, we will need to differentiate the equation implicitly with respect to x as shown:

Substituting the coordinate point (-3, 1)

Write the expression in point slope form:

Hence the equation of the tangent line to the curve is expressed as

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Let , so that differentiating both sides wrt gives

If and , the above reduces to

This is the slope of the tangent line, which has equation