Parabola and linear equation (Methods 1&2)

Av15

I am confused with this. I just started methods 1&2 as I am a year 11, and this question came up in "Solving Simultaneous linear and quadratic equation", could anyone help me with this please"

This is the question: "Find the equation of the straight line(s) which pass through the point (1, −2) and is (are)
tangent to the parabola with equation y = x2."

Please help me with this

Billzene

Av15

One equation would be -2 = m x 1 + c

Equation 2 would require some manipulation. You know that y = mx + c intersects with y = x², so mx + c = x² by substitution. Tangent implies one solution, so I'll let you use the determinant to figure this out