Consider a branch of the hypebola `x^2-2y^2-2sqrt2x-4sqrt2y-6=0` with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is (A) `1-sqrt(2/3)` (B) `sqrt(3/2) -1` (C) `1+sqrt(2/3)` (D) `sqrt(3/2)+1`

A vertex of a branch of the hyperbola x^(2)-2y^(2)-2sqrt(2)x-4sqrt(2)y-6=0 , B is one of the end points of its latuscrectum and C is the focus of the hyperbola nearest to the point A . Statement- 1 : The area of DeltaABC is ((sqrt(3))/(2)-1) sq. units. Statement- 2 : Eccentricity of the hyperbola is (sqrt(3))/(2) and length of the conjugate axis is 2sqrt(2) .

The value of sqrt(3-2\ sqrt(2)) is (a) sqrt(2)-1 (b) sqrt(2)+1 (c) sqrt(3)-sqrt(2) (d) sqrt(3)+\ sqrt(2)

Length of the latus rectum of the parabola sqrt(x) +sqrt(y) = sqrt(a) is (a) a sqrt(2) (b) (a)/(sqrt(2)) (c) a (d) 2a

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

If the angles of a triangle are in the ratio 4:1:1, then the ratio of the longest side to the perimeter is (a) sqrt(3):(2+sqrt(3)) (b) 1:6 (c) 1:2+sqrt(3) (d) 2:3

The point on the curve x^2=2y which is nearest to the point (0, 5) is(A) (2sqrt(2),4) (B) (2sqrt(2),0) (C) (0, 0) (D) (2, 2)

Consider the parabola whose focus is at (0,0) and tangent at vertex is x-y+1=0 The length of latus rectum is (a) 4sqrt(2) (b) 2sqrt(2) (c) 8sqrt(2) (d) 3sqrt(2)

The perimeter of the triangle formed by the points (0,\ 0),\ (1,\ 0) and (0,\ 1) is 1+-sqrt(2) (b) sqrt(2)+1 (c) 3 (d) 2+sqrt(2)

The equation of the base of an equilateral triangle A B C is x+y=2 and the vertex is (2,-1) . The area of the triangle A B C is: (sqrt(2))/6 (b) (sqrt(3))/6 (c) (sqrt(3))/8 (d) None of these

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is (a) 3sqrt(5) (b) 5sqrt(3) (c) 2sqrt(5) (d) 5sqrt(2)