Consider the parabola represented by the equation - 2y2 = 4x. This parabola will open to the. The equation of the directrix of the parabola is. The focus of the parabola is. NextReset

-2y2-4x, the focus of the parabola is 4x

Line: y = - 1/2x + 4 area: is 7/3 you'll have to find the slope of the tangent line first which is: y' = 2x - 2 = 2 (2) - 2 = 2 the perpendicular slope is then - 1/2 y - 3 = - 1/2 (x - 2) y = - 1/2x + 4

then you integrate, by using the line as the upper area, then subtracting the lower area parabola between 0 and 2 int (-1/2x + 4 - (x^2 - 2x + 3)) = - 1/4x^2 + 4x - x^3/3 + x^2 - 3x replace 2 for x and you will get - 1 + 8 - 8/3 + 4 - 6 12 - 29/3 = 7/3