The length of the latus rectum of the curve represented by x = 3( t + t) and y = 4( t - t) is:

Step-by-step solution

Given parametric equations are: x = 3( t + t) x 3 = t + t y = 4( t - t) y 4 = t - t Squaring and adding both equations, we get: ( x 3 )^2 + ( y 4 )^2 = ( t + t)^2 + ( t - t)^2 x^2 9 + y^2 16 = 2( ^2 t + ^2 t) x^2 9 + y^2 16 = 2 x^2 18 + y^2 32 = 1 This represents an ellipse with a^2 = 18 and b^2 = 32 . Since b^2 > a^2 , the major axis lies along the y-axis. The length of the latus rectum is given by 2a^2 b . Substituting the values: Length of latus rectum = 2 18 32 = 36 4 2 = 9 2 Answer: 9 2