Find the eccentricity of the hyperbola given by equations `x=(e^t+e^(-t))/2a n dy=(e^t-e^(-t))/3,t in Rdot`
Text Solution
Verified by Experts
Given equations `x=(e^(t)-e^(-t))/(2)and y=(e^(t)-e^(-t))/(3),` `"or "2x=e^(t)+e^(-t) and 3y=e^(t)-e^(-t)` Squaring and subtracting, we get `4x^(2)-9y^(2)=4` `"or "(x^(2))/(1)-(y^(2))/(4//9)=1` Now, `b^(2)=a^(2)(e^(2)-1)` `therefore" "e^(2)=(4)/(9)+1=(13)/(9)` `"or "e=(sqrt(13))/(3)`
Find the equation of the hyperbola given by equations x=(e^t+e^(-t))/2 and y=(e^t-e^(-t))/3,t in R .
The eccentricity of the hyperbola 2x = a(t + (1)/(t)), 2y = a(t-(1)/(t))
Find the derivative of e^(sqrt(x)) w.r.t. x .
Differentiate the following functions w.r.t. x : x(e^(x)+e^(3x))/(e^(x)+e^(-x))
Evaluate int_(-oo)^(0)(te^(t))/(sqrt(1-e^(2t)))dt
The locus of the moving point whose coordinates are given by (e^t+e^(-t),e^t-e^(-t)) where t is a parameter, is x y=1 (b) x+y=2 x^2-y^2=4 (d) x^2-y^2=2
Find the derivatives w.r.t. x : e^(x)tan x
Find the derivatives w.r.t. x : log_(x)e
Find the derivatives of each of the following functions w.r.t. x: root(3)(tan(e^(x^(2))))
The locus of the moving point whose coordinates are given by (e^t-e^(-t),e^t+e^(-t)) where t is a parameter, is (a) x y=1 (b) y+x=2 (c) y^2-x^2=4 (d) y^2-x^2=2
