Question

the line y=x+2 meets the curve y^2=4(2x+1) at A and B. Find the coordinates of the midpoint of AB​

Answer 1

Step-by-step explanation:

$If \: y = x + 2 \: meets \: the \: curve \: \\ {y}^{2} = 4(2x + 1) \: then \: it \: will \: satisfy \: \\ the \: curve. \\ = ( {x + 2)}^{2} = 4(2x + 1) \\ = {x}^{2} + 4x + 4 = 8x + 4 \\ = {x}^{2} - 4x = 0 \\ = x(x - 4) = 0 \\ x = 0 \: 4 \\ when \: x = 0 \:, y = 2 \\ whenx = 4 \:, y = 6 \\ \\ Then \: two \: points \: A(0 \:, 2) \: and \: B(4 \:, 6) \\ mid \: point \: of \: ab = ( \frac{0 + 4}{2} \:, \frac{2 + 6}{2} ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (2 \:, 4) \\ \\ Hope \: it \: will \: help \: you.$