The common tangent to the parabola `y^2=4ax` and `x^2=4ay` is

Statement I the equation of the common tangent to the parabolas y^2=4x and x^2=4y is x+y+1=0 . Statement II Both the parabolas are reflected to each other about the line y=x .

The equation of the common tangents to the parabola y = x^2 and y=- (x - 2)^2 is/are :

The equation of common tangent to the parabola y^2 =8x and hyperbola 3x^2 -y^2=3 is

Statement 1: An equation of a common tangent to the parabola y^2=16sqrt(3)x and the ellipse 2x^2+""y^2=""4 "" is ""y""=""2x""+""2sqrt(3) . Statement 2: If the line y""=""m x""+(4sqrt(3))/m ,(m!=0) is a common tangent to the parabola y^2=""16sqrt(3)x and the ellipse 2x^2+""y^2=""4 , then m satisfies m^4+""2m^2=""24 .

Find the area of the region included between the parabolas y^2= 4ax and x^2= 4ay, a gt 0 .

Show that the equation of the tangent to the parabola y^(2) = 4 ax at (x_(1), y_(1)) is y y_(1) = 2a(x + x_(1)) .

Statement I The line y=mx+a/m is tangent to the parabola y^2=4ax for all values of m. Statement II A straight line y=mx+c intersects the parabola y^2=4ax one point is a tangent line.

The number of common tangents to the circles x^2+y^2-y=0 and x^2+y^2+y=0 is :