a^(2)b^(2)t^(2)-a^(2)t=1-b^(2)t;a!=0,b!=0

Locus of centroid of the triangle whose vertices are (a cos t,a sin t),(b sin t-b cos t)and(1,0) where t is a parameter is: (3x-1)^(2)+(3y)^(2)=a^(2)-b^(2)(3x-1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)+b^(2)(3x+1)^(2)+(3y)^(2)=a^(2)-b^(2)

The three distinct point A(t_(1)^(2),2t_(1)),B(t_(2)^(2),2t_(2)) and C(0,1) are collinear,if

If A=(t^(2),2t),B=((1)/(t^(2)),-(2)/(t)) and S=(1,0) then (1)/(SA)+(1)/(SB) is equal to

Which of the following equations in parametric form can represent a hyperbolic profile, where t is a parameter: (A)x=(a)/(2)(t+(1)/(t))&y=(b)/(2)(t-(1)/(t))(B)t(x)/(a)-(y)/(b)+t=0&(x)/(a)+t(y)/(b)-1=0(C)x=e^(t)+e^(-t)&y=e^(t)-e^(-t)(D)x^(2)-6=2cos t&y^(2)+2=4cos^((t)/(2))

If A = (at^(2), 2at ) , B= ((a)/(t^(2)),- (2a)/(t) ), S(a, 0) then (1)/(SA) + (1)/(SB) =

Let A=[1-10213121] and B=[123213011]. Find A^(T),B^(T) and verify that: (A+B)^(T)=A^(T)+B^(T)( ii) (AB)^(T)=B^(T)A^(T)( iii) (2A)^(T)=2A^(T)

Prove that the point {(a)/(2)(t+(1)/(t)), (b)/(2)(t-(1)/(t))} lies on the hyperbola for all values of t(tne0) .

Prove that the point {(a)/(2)(t+(1)/(t)), (b)/(2)(t-(1)/(t))} lies on the hyperbola for all values of t(tne0) .

Prove that the point {(a)/(2)(t+(1)/(t)), (b)/(2)(t-(1)/(t))} lies on the hyperbola for all values of t(tne0) .