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`

Find the points on the parabola y^2-2y-4x=0 whose focal length is 6.

The vertex of the parabola y^2 + 4x = 0 is

The locus of the midde points ofchords of hyperbola 3x^2-2y^2+4x -6y=0 parallel to y=2x is

The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x-5y=20 to the circle x^2+y^2=9 is : (A) 20(x^2+y^2)-36+45y=0 (B) 20(x^2+y^2)+36-45y=0 (C) 20(x^2+y^2)-20x+45y=0 (D) 20(x^2+y^2)+20x-45y=0

If the line x-1=0 is the directrix of the parabola y^2-k x+8=0 , then one of the values of k is 1/8 (b) 8 (c) 4 (d) 1/4

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

If (-2,7) is the highest point on the graph of y=-2 x^2-4 a x+k , then |k| equals

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

The locus of the midpoint of the segment joining the focus to a moving point on the parabola y^2=4a x is another parabola with directrix (a) y=0 (b) x=-a (c) x=0 (d) none of these

The maximum distance of the point (4,4) from the circle x^2+y^2-2 x-15=0 is