SOLUTION: Find the x and y coordinates of the points on x^2 + y^2=16 at which the tangent line(s) are: a) horizontal b) have a slope of 1

Algebra ->  Test -> SOLUTION: Find the x and y coordinates of the points on x^2 + y^2=16 at which the tangent line(s) are: a) horizontal b) have a slope of 1      Log On


   



Question 389908: Find the x and y coordinates of the points on x^2 + y^2=16 at which the tangent line(s) are:
a) horizontal b) have a slope of 1

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a) The tangent lines are horizontal at the points (0,4) and (0,-4).
b) The tangent lines have slope 1 at the intersection points of the circle with the line y = -x. Solving:
x%5E2+%2B+y%5E2+=+x%5E2+%2B+%28-x%29%5E2+=+2x%5E2+=+16 ==> x%5E2+=+8, or
x+=+2sqrt%282%29, x+=++-2sqrt%282%29.
Then the points are (2sqrt%282%29,+-2sqrt%282%29) and (-2sqrt%282%29,+2sqrt%282%29).