The locus of the center of a circle which cuts orthogonally the parabola `y^2=4x` at (1,2) is a curve

The locus of the centre of a circle which cuts orthogonally the parabola y^(2)=4x at (1,2) will pass through(a) (3,4)(b)(4,3)(c)(5,3) (d) (2,4)

The loucs of the centre of the circle which cuts orthogonally the circle x^(2)+y^(2)-20x+4=0 and which touches x=2 is

The locus of the centre of a circle which cuts a given circle orthogonally and also touches a given straight line is (a) circle (c) parabola (b) line (d) ellipse

The locus of the centers of the circles which cut the circles x^(2) + y^(2) + 4x – 6y + 9 = 0 and x^(2) + y^(2) – 5x + 4y – 2 = 0 orthogonally is

The locus of the centre of all circle which cuts the circle x^(2)+y^(2)+4x-6y+9=0 and x^(2)+y^(2)-4x+6y+4=0 orthogonlly is

The locus of the centre of the circle which cuts the circle x^(2)+y^(2)-20x+4=0 orthogonally and touches the line x=2 is

The locus of the centre of a circle which cuts the circles 2x^(2)+2y^(2)-x-7=0 and 4x^(2)+4y^(2)-3x-y=0 orthogonally is a straight line whose slope is (A)-1 (B) 1(C)-2(D)-(5)/(2)

If the locus of centres of a family of circles passing through the vertex of the parabola y^(2)=4ax and cutting the parabola orthogonally at the other point of intersection is 2y^(2)(2y^(2)+x^(2)-12ax)=ax(kx-4a)^(2) ,then find the value of k.