If `(x_1-x_2)^2+(y_1-y_2)^2=a^2`, `(x_2-x_3)^2+(y_2-y_3)^2=b^2`, `(x_3-x_1)^2+(y_3-y_1)^2=c^2`, and `2s=a+b+c` then what willl be the value of `1/4|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|^2`

If a x_1^2+b y_1^2+c z_1^2=a x_2 ^2+b y_2 ^2+c z_2 ^2=a x_3 ^2+b y_3 ^2+c z_3 ^2=d ,a x_2 x_3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f, then prove that |(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3,y_3,z_3)|=(d-f){((d+2f))/(a b c)}^(1//2)

If (x_i ,y_i),i=1,2,3, are the vertices of an equilateral triangle such that (x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2, then find the value of (x_1+x_2+x_3)/(y_1+y_2+y_3) .

If x(2+sqrt3)=y(2-sqrt3)=1 , then the value of 1/(x+1)+1/(y+1) is :

If y=int1/(1+x^2)^(3/2)dx and y=0 when x=0 , then value of y when x=1 is

If A (x_1,y_1) , B(x_2,y_2) and C (x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a unit , then prove that, |{:(x_1,y_1,2),(x_2,y_2,2), (x_3,y_3,2):}|^2=3a^4

IF x^2+y^2=a^2 , show that, (1+y_1^2)^(3/2)/y_2=-a

If x^2+y^2=1 and P=(3x-4x^3)^2+(3y-4y^3)^2 then P is equal to

If tan^-1(1/y)=-pi+cot^-1 y, where y=x^2-3x+2, then find the value of x

If x_1, x_2 , x_3 and y_1 , y_2 , y_3 are both in G.P. with the same common ratio, then the points (x_1 , y_1),(x_2 , y_2) and (x_3 , y_3)

IF x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then -