Sketch the parabolas ` y^(2) = 8 x and x^(2) = 8y. ` find the area bounded between the parabola.

Find the area bounded by x=2y-y^2

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is

Sketch the curve y = x^(3) find the area bounded by the above curve, the a-axis between the ordinates x = 02 and x = 1

The vertex of the parabola x^(2)=8y-1 is :

Draw a rough sketch of the curve y=(x^2+3x+2)/(x^2-3x+2) and find the area of the bounded region between the curve and the x-axis.

Length of the focal chord of the parabola (y +3)^(2) = -8(x-1) which lies at a distance 2 units from the vertex of the parabola is

Show that the locus of a point that divides a chord of slope 2 of the parabola y^2=4x internally in the ratio 1:2 is parabola. Find the vertex of this parabola.

(i) Find the points of intersection of the parabola y ^(2) = 8x and the line y = 2x . (ii) Find, using integration, the area enclosed between the line and the parabola.

Find the vertex of the parabola x^2=2(2x+y)