Find the coordinates of the points where the line 2y=x-1 meets the curve x2+y2=29?

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Answer 1 · 2018-03-04T17:36:32

The points are, #(-23/5,-14/5)# and #(5,2)#

Write the linear equation as:

#x = 2y+1#

Substitute for x into the equation of the circle:

#(2y+1)^2 + y^2 = 29#

Expand the square:

#4y^2+4y+1+y^2=29#

Combine like terms:

#5y^2+4y-28=0#

Factor:

#(5y+14)(y-2)=0#

The roots are:

#y=-14/5# and #y=2#

Use #x=2y+1# to find the corresponding x values:

#x=2(-14/5)+1# and #x=2(2)+1#

#x=-23/5# and #x=5#