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^2-4kx=0` b) `x^2+y^2-4ky=0` c) `2x^2+4y^2-9kx=0` d) `4x^2-y^2+4kx=0`

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

The straight lines joining any point P on the parabola y^2=4a x to the vertex and perpendicular from the focus to the tangent at P intersect at Rdot Then the equation of the locus of R is (a) x^2+2y^2-a x=0 (b) 2x^2+y^2-2a x=0 (c) 2x^2+2y^2-a y=0 (d) 2x^2+y^2-2a y=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

In triangle A B C , the equation of side B C is x-y=0. The circumcenter and orthocentre of triangle are (2, 3) and (5, 8), respectively. The equation of the circumcirle of the triangle is a) x^2+y^2-4x+6y-27=0 b) x^2+y^2-4x-6y-27=0 c) x^2+y^2+4x-6y-27=0 d) x^2+y^2+4x+6y-27=0

The equation of the circle passing through the point of intersection of the circles x^2+y^2-4x-2y=8 and x^2+y^2-2x-4y=8 and the point (-1,4) is (a) x^2+y^2+4x+4y-8=0 (b) x^2+y^2-3x+4y+8=0 (c) x^2+y^2+x+y=0 (d) x^2+y^2-3x-3y-8=0

The equation of the circle which has normals (x-1).(y-2)=0 and a tangent 3x+4y=6 is (a) x^2+y^2-2x-4y+4=0 (b) x^2+y^2-2x-4y+5=0 (c) x^2+y^2=5 (d) (x-3)^2+(y-4)^2=5

Find the angle of intersection of the curve x^2+y^2-4x-1=0 and x^2+y^2-2y-9=0 .

If points A and B are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

2x-y=4,x-2y+1=0

The point of intersection of the tangents of the parabola y^2=4x drawn at the endpoints of the chord x+y=2 lies on (a) x-2y=0 (b) x+2y=0 (c) y-x=0 (d) x+y=0