If `y=2` is the directrix and `(0,1)` is the vertex of the parabola `x^2+lambday+mu=0` , then (a)`lambda=4` (b) `mu=8` (c) `lambda=-8` (d) `mu=4`

The vertex of the parabola x^(2)+2y=8x-7 is

The vertex of the parabola x^(2)-6x+4y+1=0 is

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 (a) 1/8 (b) 8 (c) 4 (d) 1/4

The centre of the circle lambdax^2+(2lambda-3)y^2-4x+6y-1=0 is

If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x in the largest possible interval (-2,-2/3)dot Then (a ) lambda=4 (b) lambda=2 (c) lambda=-1 (d) lambda has no real value

If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is (a)12 (b) -12 (c) 24 (d) -24

The equation of the directrix of the parabola y^2+4y+4x+2=0 is (a) x=-1 (b) x=1 x=-3/2 (d) x=3/2

If x=(3)/(k) be the equation of directrix of the parabola y ^(2) + 4 y + 4 x + 2 = 0 then , k is _

Portion of asymptote of hyperbola x^2/a^2-y^2/b^2 = 1 (between centre and the tangent at vertex) in the first quadrant is cut by the line y + lambda(x-a)=0 (lambda is a parameter) then (A) lambda in R (B) lambda in (0,oo) (C) lambda in (-oo,0) (D) lambda in R-{0}

x - 1 = 0 is the equation of directrix of the parabola y^(2) - kx + 8 = 0 . Then the value of k is _