Find the equation of the tangent line to the curve

Question

2(x^2+y^2)^2 = 25(x^2-y^2) at the point ( 3 , -1 ). The equation of this tangent line can be written in the form y = mx+b, find m and b
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Answer 1

The equation is

Apply formula :

Subtract from each side

Apply derivetive

Above equation passes through the point (3, -1)

Slope and point (3, -1), than the line equation is

Subtract 1 from each side

Apply distributive property :

Above equation is similar to y = mx+b

Therefore slope and constant (b) =