Question

The line 2x - y + 4 = 0 cuts the parabola y2 = 8x in P and Q. The midpoint of PQ is

Answer 1

Answer:

$Hence \: \: the \: \: given \: \: equation \: \: is \: \: wrong.$

Step-by-step explanation:

$Given, \\ line \: \: \: 2x - y + 4 = 0 \\ y = 2x + 4 \: \: and \\ parabola \: \: \: {y}^{2} = 8x \\ On \: \: solving \: \: both \: \: the \: \: equations \\ putting \: \: value \: \:of \: y \\ (2x + 4)^{2} = 8x \\ 4 {x}^{2} + 16x + 16 = 8x \\ 4 {x}^{2} + 8x + 16 = 0 \\ (2x)^{2} + 2 \times 2x \times 1 + {1}^{2} + 15 = 0 \\ (2x + 1)^{2} = - 15 \\ 2x + 1 = \sqrt{ - 15} \\ The \: \: value \: \: of \: \: x \: \: comes \: \: \: \: to \: \: be \: \: an \: \: imaginary \: \: number, \\ Hence \: \: the \: \: given \: \: equation \: \: is \: \: wrong.$