Consider the curve `C_(1):x^(2)-y^(2)=1` and `C_(2):y^(2)=4x` then The point of intersection of directrix of the curve `C_(2)` with `C_(1)`

Consider the curve C_(1):x^(2)-y^(2)=1 and C_(2):y^(2)=4x then ,The number of lines which are normal to C_(2) and tangent to C_(1) is

Consider the two curves C_(1);y^(2)=4x,C_(2)x^(2)+y^(2)-6x+1=0 then :

From the point A, common tangents are drawn to the curve C_(1):x^(2)+y^(2)=8 and C_(2):y^(2)=16x. The y- intercept of common tangent between C_(1) and C_(2) having negative gradients,is

The equation of a circle C_(1) is x^(2)+y^(2)=4 The locus of the intersection of orthogonal tangents to the circle is the curve C_(2) and the locus of the intersection of perpendicular tangents to the curve C_(2) is the curve C_(3), Then

The equation of a circle is x^(2)+y^(2)+14x-4y+28=0. The locus of the point of intersection of orthoonal tangents to C_(1) is the curve C_(2) and the locus of the point of intersection of perpendicular tangents to C_(2) is the curve C_(3) then the statement(s) which hold good?

if two curves C_(1):x=y^(2) and C_(2):xy=k cut at right angles,then value of k is :

Consider the curves C_(1) = y - 4x + x^(2) = 0 and C_(2) = y - x^(2) + x = 0 The raio in which the line y = x divide the area of the region bounded by the curves C_(1) = 0 and C_(2) = 0 is

Consider two circles C_(1):x^(2)+y^(2)-1=0 and C_(2):x^(2)+y^(2)-2=0. Let A(1,0) be a fixed point on the circle C_(1) and B be any variable point on the circle C_(1) and B be any variable curve C_(2) again at C. Which of the following alternative(s) is/are correct?