What is the total number of points of intersection of the graphs of the equations #2x^2-y^2=8, y=x+2#?

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Answer 1 · 2017-05-03T10:03:22

We have two points #(6,8)# and #(-2,0)#

To find number of points of intersection, we should solve these pair of equations.

As #y=x+2#, we have #2x^2-(x+2)^2=8#

or #2x^2-x^2-4x-4=8# or #x^2-4x-12=0#

or #x^2+2x-6x-12=0#

or #x(x+2)-6(x+2)=0#

or #(x-6)(x+2)=0#

and hence #x=6# or #-2#

putting these values in #y=x+2#, we get #y=8# or #0#

Hence, we have two points #(6,8)# and #(-2,0)#

graph{(y-x-2)(2x^2-y^2-8)=0 [-8, 12, -0.6, 9.4]}