Prove that the locus of the circumcentre of the variable triangle having sides y-axis, y = 2 and lx + my = 1 where (l, m) lies on the parabola `y^(2)=4ax`, is also a parabola

The locus of the circumcenter of a variable triangle having sides the y-axis, y=2, and lx+my=1, where (1,m) lies on the parabola y^(2)=4x , is a curve C. The coordinates of the vertex of this curve C is

The locus of the circumcenter of a variable triangle having sides the y-axis, y=2, and lx+my=1, where (1,m) lies on the parabola y^(2)=4x , is a curve C. The length of the smallest chord of this C is

The locus of the circumcenter of a variable triangle having sides the y-axis, y=2, and lx+my=1, where (1,m) lies on the parabola y^(2)=4x , is a curve C. The curve C is symmetric about the line

Let C be the locus of the circumcentre of a variable traingle having sides Y-axis ,y=2 and ax+by=1, where (a,b) lies on the parabola y^2=4lamdax . For lamda=1/32 , the length of smallest focal chord of the curve C is

The pole of the line lx+my+n=0 with respect to the parabola y^(2)=4ax, is

The line lx+my+n=0 is a normal to the parabola y^(2)=4ax if

If lx + my + n = 0 is tangent to the parabola x^(2)=y , them

Equation of normal to the parabola y^(2)=4ax having slope m is