Find equation of tangent line to (x-1)^2 + (y+1)^2 = 2 at point (2,-2)

Question

Find equation of tangent line to (x-1)^2 + (y+1)^2 = 2 at point (2,-2)

 

Can someone explain the steps such as find slope...

 

I'm confused on the perpindicular of the line to get the tangent equation.  

 

 

Answer 1

To find the slope of an equation at a point, you generally have to find its derivative. However, this question becomes much, MUCH easier if you graph it out first.

 

If you graph it out, you'll find that this is the equation for a circle. The slope at a point of a circle is perpendicular to the line that you draw from the center of the circle to that point. So find the point that equals the center, create a line from that point to (2,-2) and solve for the equation.

 

Remember that the equation for a circle is: (x-a)² + (y-b)² = r² where (a,b) is the center of the circle and r is the radius.

 

Hope this helps!