Find the coordinates of all points on the graph of y = 1 - x^2 at which the tangent line passes through the point (2,0)?

1 Answer
Nov 20, 2017

Points are #(-1,0)# and #(1,0)#

Explanation:

As the function is #y=1-x^2#, the slope of the tangent is

#y'=-2x#

and the equation of line passing through #(0,2)# is

#y-2=-2x(x-0)# or #y=-2x^2+2#

Hence the points, at which tangentline passes through #(2,0)# are given by

#-2x^2+2=1-x^2#

or #x^2-1=0# i.e. #x=+-1# and points are #(-1,0)# and #(1,0)#

and tangents are #y-2=-2(-1)x# i.e. #2x-y+2=0#

and #y-2=-2(1)x# i.e. #2x+y-2=0#

graph{(y+x^2-1)(2x-y+2)(2x+y-2)=0 [-5.104, 4.896, -1.48, 3.52]}