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`

Consider a branch of the hyperbola : x^2 -2y^2-2sqrt2x-4sqrt2y-6=0 with vertex at the point A. Let B be one of the end points of the latus -rectum. If C is the focus of the hyperbola nearest to the point A , then the area of the traingle ABC is :

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) .

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) .

If A(1,-1,2),B(2,1,-1)C(3,-1,2) are the vertices of a triangle then the area of triangle ABC is (A) sqrt(12) (B) sqrt(3) (C) sqrt(5) (D) sqrt(13)

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

If the point (a,b) on the curve y= sqrt(x) is close to the point (1,0) , then the value of ab is a) 1/2 b) (sqrt2)/(2) c) 1/4 d) (sqrt2)/(4)

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)

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 shortest distance from the point (1,2,-1) to the surface of the sphere x^(2)+y^(2)+z^(2)=54 is a) 3sqrt(6) b) 2sqrt(6) c) sqrt(6) d)2