Search for question
Question

3. The parametric equations of a curve are x=t+\frac{3}{t}, y=t-\frac{3}{t}, \quad(t \neq 0) \text { The gradient of the curve } \frac{d y}{d x}=\frac{t^{2}+3}{t^{2}-3} \text {. } (a) Determine the coordinates of the points on the curve where the gradient is equal to 2. (b) Express x² and y² in terms of t and hence determine a Cartesian equation of thecurve. (c) The point P on the curve is where t = 1. (i) Find the equation of the normal to the curve at the point P. (ii) Determine the coordinates of the point where the normal to the curve at P cuts the-curve again.

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8