Question

find the equation of the tangent at the point (a,b) to the curve XY=c^2​

Answer 1

Answer:

Step-by-step explanation:

xy = c²

differentiating the above curve at (a,b) we get slope of that tangent at that point

x*dy/dx + y = 0

x*dy/dx = -y

dy/dx= -y/x

 slope at the point (a,b)

dy/dx = -b/a

the equation of the tangent at (a,b)

(y-b) = -b/a (x-a)

a(y-b)= -b(x-a)

ay-ab = -bx +ab

bx+ay -2ab = 0  

This is equation of tangent at the point (a,b)