Shift the origin to a suitable point so that the equation `y^2+4y+8x-2=0` will not contain a term in `y` and the constant term.

Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

If O is origin and R is a variable point on y^(2)=4x , then find the equation of the locus of the mid-point of the line segment OR.

If O is origin and R is a variable point on y^2=4x , then find the equation of the locus of the mid-point of the line segmet OR .

Statement 1 : The equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0 is x-y=0 . Statement 2 : y+x=0 is the common chord of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0

Find the equations of the tangents drawn to the curve y^2-2x^3-4y+8=0.

Identify the type of conic for the following equation. 9x^(2)-4y^(2)-18x+8y-25=0

If origin is shifted to (-2,3) then transformed equation of curve x^2 +2y-3=0 w.r.t. to (0,0) is

The second degree equation x^2+4y^2-2x-4y+2=0 represents

Find the 4^th term in the expansion of (x-2y)^12 .