Find the equation of the tangent line at the given point on

Find the equation of the tangent line at the given point on the following curve. X^2 + y^2 = 2, (1, -1). The equation of the tangent line to the point (1, -1) is y =

Solution

x^2 + y^2= 2

here the centre is (0,0) and radius is sqrt 2

And radius is always perpendicular to the tangent

SO first we have to find the slope of radius where centre is (0,0) and point is (1,-1)

Therefore slope= -1-0/1-0=-1

Slope of radius=-1

And radius is perpendicular on tangent

therefore slope of tangent=1

Now we use point slope form to find the equation of tangent

y-y0=m(x-x0)

y-(-1)=1(x-1)

y+1=x-1

y=x-2 and that\'s the required equation.