The locus of a point on the variable parabola `y^2=4a x ,` whose distance from the focus is always equal to `k ,` is equal to (`a` is parameter) (a)`4x^2+y^2-4k x=0` (b)`x^2+y^2-4k x=0` (c)`2x^2+4y^2-9k x=0` (d) `4x^2-y^2+4k x=0`

If y=2x+k is a tangent to the curve x^(2)=4y , then k is equal to

If the line x-3y+k=0 touches the parabola 3y^(2)=4x then the value of k is

The equation of the common tangent to parabola y^(2)=4x and x^(=)4y is x+y+(k)/(sqrt(3))=0, then k is equal to

The mirror image of any point on the directrix of the parabola y^(2)=4(x+1) in the line mirror x+2y=3-0 lies on 3x-4y+4k=0, Then k=

If the area enclosed by y^(2)=2x and x^(2)+4+4x=4y^(2) is k square units, then the value of 3k is equal to

Distance between two parallel planes 2x+y+2z=8 and 4x+2y+4z+5=0 is 2k then k is equal to

If equation of directrix of the parabola x^(2)+4y-6x+k=0 is y+1=0, focus is (a,b) and vertex is (c,d), then (k+a+c+3b+3d) is equal to

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (A) x^2 + y^2 - 2x - 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x + 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0