If the normal to the given hyperbola at the point `(c t , c/t)` meets the curve again at `(c t^(prime), c/t^(prime)),` then (A) `t^3t^(prime)=1` (B) `t^3t^(prime)=-1` (C) `t t^(prime)=1` (D) `t t^(prime)=-1`

if the normal at the point t_(1) on the parabola y^(2) = 4ax meets the parabola again in the point t_(2) then prove that t_(2) = - ( t_(1) + 2/t_(1))

Find the tangent and normal to the following curves at the given points on the curve. x = cos t, y = 2 sin^(2) t " at" t= (pi)/(3)

If a function is represented parametrically be the equations x=(1+(log)_e t)/(t^2); y=(3+2(log)_e t)/t , then which of the following statements are true? (a) y^('')(x-2x y^(prime))=y (b) y y^(prime)=2x(y^(prime))^2+1 (c) x y^(prime)=2y(y^(prime))^2+2 (d) y^('')(y-4x y^(prime))=(y^(prime))^2

Find the locus of the point (t^2-t+1,t^2+t+1),t in Rdot

If the normals at points t_1a n dt_2 meet on the parabola, then t_1t_2=1 (b) t_2=-t_1-2/(t_1) t_1t_2=2 (d) none of these

Let Aa n dB be two events such that P(AnnB^(prime))=0. 20 ,P(A^(prime)nnB)=0. 15 ,P(A^(prime)nnB^(prime))=0. 1 ,t h e nP(A//B) is equal to 11//14 b. 2//11 c. 2//7 d. 1//7

The slope of the tangent to the curve x= t^(2)+3t-8,y=2t^(2)-2t-5 at the point (2,-1) is

Statement 1: If both functions f(t)a n dg(t) are continuous on the closed interval [1,b], differentiable on the open interval (a,b) and g^(prime)(t) is not zero on that open interval, then there exists some c in (a , b) such that (f^(prime)(c))/(g^(prime)(c))=(f(b)-f(a))/(g(b)-g(a)) Statement 2: If f(t)a n dg(t) are continuou and differentiable in [a, b], then there exists some c in (a,b) such that f^(prime)(c)=(f(b)-f(a))/(b-a)a n dg^(prime)(c)(g(b)-g(a))/(b-a) from Lagranes mean value theorem.

If the sequence t_(1), t_(2), t_(3), … are in A.P. then the sequence t_(6), t_(12), t_(18),… is