What are the points of contact between the line x -2y equals 1 and the curve 4y squared -3x squared equals 1?

What are the points of contact between the line x -2y equals 1 and the curve 4y squared -3x squared equals 1?
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If: x-2y = 1 Then: x^2 = 4y^2 +4y+1 If: 4y^2 -3x^2 = 1 Then: 4y^2 -3(4y^2 +4y+1) = 1 Removing brackets: 4y^2 -12y^2 -12y -3 = 1 Transposing terms: -8y^2 -12y -4 = 0 Dividing all terms by -4: 2y^2 +3y +1 = 0 Factorizing the above: (2y+1)(y+1) = 0 meaning y = -1/2 or -1 By substitution into original linear equation points of contact are at: (0, -1/2) and (-1, -1)
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