The equation of the incircle of equilateral triangle `A B C` where `B-=(2,0),C-=(4,0),` and `A` lies in the fourth quadrant is: (a) `x^2+y^2-6x+(2y)/(sqrt(3))+9=0` (b) `x^2+y^2-6x-(2y)/(sqrt(3))+9=0` (c) `x^2+y^2+6x+(2y)/(sqrt(3))+9=0` (d) none of these

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

The equation of a circle of radius 1 touching the circles x^2 + y^2 - 2 |x| = 0 is: (A) x^2 + y^2 + 2sqrt(3x) - 2 = 0 (B) x^2 + y^2 - 2sqrt(3)y+2=0 (C) x^2 + y^2 + 2sqrt(3) y + 2 = 0 (D) x^2 + y^2 + 2 sqrt(3) x + 2 = 0

The equation of the circle touching Y-axis at (0,3) and making intercept of 8 units on the axis (a) x^(2)+y^(2)-10x-6y-9=0 (b) x^(2)+y^(2)-10x-6y+9=0 (c) x^(2)+y^(2)+10x-6y-9=0 (d) x^(2)+y^(2)+10x+6y+9=0

The latus rectum of the conic 3^(2)+4y^(2)-6x+8y-5=0 is 3b.(sqrt(3))/(2)c(2)/(sqrt(3))d. none of these

Find common tangent of the two curve y^(2)=4x and x^(2)+y^(2)-6x=0 (a) y=(x)/(3)+3 (b) y=((x)/(sqrt(3))-sqrt(3)) (c) y=(x)/(3)-3 (d) y=((x)/(sqrt(3))+sqrt(3))

A vertex of an equilateral triangle is at (2, 3), and th equation of the opposite side is x+y=2 , then the equaiton of the other two sides are (A) y=(2+sqrt(3)) (x-2), y-3=2sqrt(3)(x-2) (B) y-3=(2+sqrt(3) (x-2), y-3= (2-sqrt(3) (x-2) (C) y+3=(2-sqrt(3)(x-2), y-3=(2-sqrt(3) (x+2) (D) none of these

The equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0 and x^2 + y^2 + 2x - 6y - 6=0 and having its centre on y=0 is : (A) 2x^2 + 2y^2 + 8x + 3 = 0 (B) 2x^2 + 2y^2 - 8x - 3 = 0 (C) 2x^2 + 2y^2 - 8x + 3 = 0 (D) none of these

The equation of incircle of the triangle formed by common tangents to the circles x^(2)+y^(2)=4 and x^(2)+y^(2)-6x+8=0 is

An equilateral triangle whose two vertices are (-2, 0) and (2, 0) and which lies in the first and second quadrants only is circumscribed by a circle whose equation is : (B) sqrt(3)x^2 + sqrt(3)y^2 - 4x - 4 sqrt(3)y = 0 (C) sqrt(3)x^2 + sqrt(3)y^2 - 4y + 4 sqrt(3)y = 0 (D) sqrt(3)x^2 + sqrt(3)y^2 - 4y - 4 sqrt(3) = 0

Let vertices of the triangle ABC is A(0,0),B(0,1) and C(x,y) and perimeter is 4 then the locus of C is : (A)9x^(2)+8y^(2)+8y=16(B)8x^(2)+9y^(2)+9y=16(C)9x^(2)+9y^(2)+9y=16(D)8x^(2)+9y^(2)-9x=16