2x +1 = 5x-2
2x +3= 5x
3 = 3x
x=1
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If y = 2x+1 is a tangent line to the circle 5y^2 +5x^2 = 1 then the point of contact is at (-2/5, 1/5) because it has equal roots
5x2 + 2x - 3 = 0 5x2 + 5x - 3x - 3 = 0 5x(x + 1) - 3(x + 1) = 0 (5x - 3)(x + 1) = 0 So 5x - 3 = 0 or x + 1 = 0 ie x = 3/5 or x = -1
5y2 + 5x2 = 1 Substitute y = 2x + 1 into this equation: 5*(2x + 1)2 + 5x2 = 1 5*(4x2 + 4x + 1) + 5x2 - 1 = 0 25x2 + 20x + 4 = 0 which factorises to (5x + 2)2 = 0 Therefore x = -2/5 And then y = 2x + 1 gives y = 1/5 So the two points of intersection are coincident, at (-2/5, 1/5)
It is 4x^2 + 10x - 1
-2x plus 3y equals 1