Find the equations of the lines that are tangent and normal to the curve e^ x + y^ 2 = 2 at the point (0, 1).

Question

Can someone please help me with this.

Answer 1

eˣ+y²=2,

eˣ+2yy'=0,

2yy'=-eˣ.

At (0,1): 2y'=-1, y'=-½, so the tangent line has a slope -½, and the normal has a slope -1/(-½)=2.

Use slope/intercept to get the tangent line and normal line equations:

TANGENT: y-1=-x/2, y=-x/2+1

NORMAL: y-1=2x, y=2x+1

Curve is in red; the tangent line is blue and the normal line is green.