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

The focus of the parabola y^(2)-4y-8x+4=0 is,

The focus of the parabola y^(2)-4y-8x-4=0 is

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

The tangent and the normal at the point A-= (4, 4) to the parabola y^2 = 4x , intersect the x-axis at the point B and C respectively. The equation to the circumcircle of DeltaABC is (A) x^2 + y^2 - 4x - 6y=0 (B) x^2 + y^2 - 4x + 6y = 0 (C) x^2 + y^2 + 4x - 6y = 0 (D) none of these

Let P be any moving point on the circle x^2+y^2-2x=1. A B be the chord of contact of this point w.r.t. the circle x^2+y^2-2x=0 . The locus of the circumcenter of triangle C A B(C being the center of the circle) is a. 2x^2+2y^2-4x+1=0 b. x^2+y^2-4x+2=0 c. x^2+y^2-4x+1=0 d. 2x^2+2y^2-4x+3=0

From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 . The locus of the midpoints of the chords is (a) x^2+y^2-5x-4y+6=0 (b) x^2+y^2+5x-4y+6=0 (c) x^2+y^2-5x+4y+6=0 (d) x^2+y^2-5x-4y-6=0

Let P be the point on the parabola, y^2=8x which is at a minimum distance from the centre C of the circle, x^2+(y+6)^2=1. Then the equation of the circle, passing through C and having its centre at P is : (1) x^2+y^2-4x+8y+12=0 (2) x^2+y^2-x+4y-12=0 (3) x^2+y^2-x/4+2y-24=0 (4) x^2+y^2-4x+9y+18=0

Let x+y=k be a normal to the parabola y^(2)=12x . If p is the length of the perpendicular from the focus of the parabola onto this normal then 4k-2 p^(2) =?

Equation of line touching both parabolas y^(2)=4x and x^(2) = -32y is a) x+2y + 4 =0 b) 2x +y4 =0 c) x-2y-4 =0 d) x-2y+4 =0