# SOLUTION: Hello, i have been given this maths question, please could you help me solve it. I have tried putting it into a quadratic equation then i realised that it cannot be factorised. The

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Hello, i have been given this maths question, please could you help me solve it. I have tried putting it into a quadratic equation then i realised that it cannot be factorised. The      Log On

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 Question 578107: Hello, i have been given this maths question, please could you help me solve it. I have tried putting it into a quadratic equation then i realised that it cannot be factorised. The question is: prove that the line y+x=-2 is a tangent to the curve y^2 = 8x Thank youAnswer by Edwin McCravy(9716)   (Show Source): You can put this solution on YOUR website!prove that the line y+x=-2 is a tangent to the curve y^2 = 8x. ```A line which intersects a parabola exactly once and which is not parallel to the axis of symmetry, is tangent to the parabola. y + x = -2 is a tangent to the curve y² = 8x The axis of symmetry of that parabola is the x-axis, and the line y + x = -2 is not parallel to the x-axis, so if it intersects the parabola exactly once, then it is tangent to the parabola. We solve the equation of the line for y y + x = -2 - x y = -2 - x And we substitute (-2 - x) for y in y² = 8x (-2 - x)² = 8x 4 + 4x + x² = 8x x² - 4x + 4 = 0 (x - 2)(x - 2) = 0 x - 2 = 0, x - 2 = 0 x = 2 x = 2 Th fact that -2 is a double root for x shows that there is just one point of intersection and so the line is tangent to the parabola at the point were x = 2, which has y-coordinate y = -2 - (2) = -4 or the point (2,-4) is the point of tangency. Edwin```