An equilateral triangle `S A B` is inscribed in the parabola `y^2=4a x` having its focus at `Sdot` If chord `A B` lies towards the left of `S ,` then the side length of this triangle is (a)`2a(2-sqrt(3))` (b) `4a(2-sqrt(3))` (c)`a(2-sqrt(3))` (d) `8a(2-sqrt(3))`

An equilateral triangle is inscribed in the parabola y^(2) = 4ax whose vertex is at the vertex of the parabola. Find the length of its side.

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

In an equilateral triangle, three coins of radii 1 unit each are kept so that they touch each other and also the sides of the triangle. The area of the triangle is (fig) 4:2sqrt(3) (b) 6+4sqrt(3) 12+(7sqrt(3))/4 (d) 3+(7sqrt(3))/4

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

An isosceles triangle A B C is inscribed in a circle x^2+y^2=a^2 with the vertex A at (a ,0) and the base angle Ba n dC each equal 75^0 . Then the coordinates of an endpoint of the base are. (a) (-(sqrt(3a))/2, a/2) (b) (-(sqrt(3a))/2, a) (c) (a/2,(sqrt(3a))/2) (d) ((sqrt(3a))/2,-a/2)

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

A right-angled triangle A B C is inscribed in parabola y^2=4x , where A is the vertex of the parabola and /_B A C=pi/2dot If A B=sqrt(5), then find the area of A B Cdot

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4