Parametric equations

Find an expression for the position vector of the particle at time t s.

Find the Cartesian equation of the path of the particle.

in Fig. C2.

The parametric equations of a curve are

x = 2 + 5 cos θ and y = 1 + 5 sin θ, where 0 ⩽ θ ⩽ 2 π.

Determine the cartesian equation of the curve.

Hence or otherwise, find the equation of the tangent to the curve at the point (5, - 3), giving

your answer in the form ax + by + c = 0, where a, b and c are integers to be determined.

In this question you must show detailed reasoning. Fig. 10 shows the curve given parametrically by the equations x = y = - for t > 0.

Find the coordinates of the point on the curve at which the tangent to the curve is parallel to

the line 4 y + x = 1.

Find the cartesian equation of the curve. Give your answer in factorised form.

Fig. 12 shows a curve C with parametric equations x = 4t², y = 4t. The point P, with parameter t is a general point on the curve. Q is the point on the line x + 4 = 0 such that PQ is parallel to the x-axis. R is the point (4, 0).

Show algebraically that P is equidistant from Q and R.

Find a cartesian equation of C.