The correct choice is (c) x – y + 2 = 0
The best explanation: Equation of the given parabola is, y^2 = 8x ……….(1)
Differentiating both sides with respect to x,
2y(dy/dx) = 8
Or dy/dx = 4/y
Thus, equation of the tangent to the parabola (1) at (x1, y1) = (2t^2, 4t) is,
y – y1 = [dy/dx](x1, y1) (x – 2t^2)
y – 4t = [dy/dx](2(t^2), 4t) (x – 2t^2)
Putting the value of y = 4t in the equation dy/dx = 4/y, we get,
y – 4t = 4/4t(x – 2t^2) ……….(2)
If the tangent to the parabola y^2 = 8x, which is inclined at an angle of 45° with the x axis,
Then, slope of tangent (2) = tan 45° = 1
Thus, 4/4t = 1
Or t = 1
Thus, required equation of the tangent is,
y– 4 = 1(x – 2)
Putting, t = 1 in (2),
So, x – y + 2 = 0