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 : y=x^2-2x +3 .

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

Sketch the curve y=x^3-4x .

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 = 9y and y^2 = 9x . 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.

In the following, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas. 9y^2 - 4x^2 = 36

Sketch the graphs of the following pair of equations on the same axes : y = cos 2x, y= cos (2x-pi) .