It is given that x = 5*cos t and y = 3*sin t. We have to find the equation of the tangent if t = pi/4
When t = pi/4 , x = 5*(1/sqrt 2) and y = 3/sqrt 2
dx/dt = -5*sin t and dy/dt = 3*cos t
dy/dx = (dy/dt)/(dx/dt)
=> 3*cos t/ -5*sin t
=> (-3/5)/tan t
at t = pi/4
=> -3/5
The equation of the tangent is (y - 3/sqrt 2)/(x - 5/sqrt 2) = -3/5
=> 5y - 15/sqrt 2 = -3x + 15/sqrt 2
=> 3x + 5y - 30/sqrt 2 = 0
The equation of the tangent is 3x + 5y - 30/sqrt 2 = 0