Find the foci, vertices, directrices, and axes of following parabola. Also draw their rough sketches :
` y=x^2-2x +3` .

Find the foci, vertices, directrices, and axes of following parabola. Also draw their rough sketches : y=- 4x^2 + 3x .

Find the foci, vertices, directrices, and axes of following parabola. Also draw their rough sketches : x^2+ 2y -3x+5=0 .

Find the area of the region enclosed between the parabolas x^2 = 9y and y^2 = 9x . Also draw its rough sketch.

Find the area of the region enclosed between the parabolas x^2 = 4y and y^2 = 4x . Also draw its rough sketch.

Find the area of the region enclosed between the parabolas x^2 = 16y and y^2 = 16x . Also draw its rough sketch.

Find the lengths of the major and minor axes, co-ordinates of the foci, vertices, the eccentricity and equations of the directrices for the ellipse 9x^2+ 16y^2 = 144 .

Using integration, find the area of the region bounded by the following curves, after making a rough sketch:(ii) y=1+|x+1|,x=-2,x=3,y=0.

Using integration, find the area of the region bounded by the following curves, after making a rough sketch: (i) y=1+|x+1|,x=-3,x=3,y=0.