Find the ratio of the areas in which the curve `y=[x^3/100+x/35]` divides the circle `x^2+y^2-4x+2y+1=0`

The figure into which the curve y^(2)=6x divides the circle x^(2)+y^(2)=16 are in the ratio

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

Find the equation of the circle passing through the centre of the circle x^(2)+y^(2)+8x+10y-7=0 and concentric with the circle x^(2)+y^(2)-4x-6y=0

Find the ratio in which the area bounded by the curves y^(2)=12x and x^(2)=12y is divided by the line x=3.

Find the area of the region bounded by the curves 2y^2=x, 3y^2=x+1, y=0 .

Find the area of the region bounded by the curves y=x^(2)+2y=x,x=0 and x=3

Find the equation of the circle which is concentric with the circle x^2 +y^2 - 4x+6y-3=0 and the double of its area.

Find the equation of the tangent line to the curve y=(3x^2-1)/x at the point (1,2) is (a) 4x-y-1=0 (b) 4x+y+2=0 (c)x-y-1=0 (d) 4x-y-2=0