Find the Lines that are Tangent and Normal to the Curve at the given points.
x^2+xy-y^2 = 11 , (3,1)
a) Give the equation that is tangent to the curve.
2x+(x dy/x + y dy/x) - 2y dy/dx = 0
(x-2y)dy/dx + 2x+y = 0
(x-2y)dy/dx = -2x-y
dy/dx = -2x-y/x-2y
dy/dx= -2(3)-1 / 3-2(1) = 7/1
y= y1 + m(x-x1)
y= 1 + 7/1(x-3) = ??? (I have tried many problems like this in Mymathlab and always get wrong this part)
b) Give the Equation that is Normal to the Curve.
y=1-7/1(x-3)
y= (also can't get this part right)
Please if Someone can show step by step how to do this problem I will appreciated.