1. Find the equation of the tangent to the circle x2 + y2 = 25 at the point (3, 4) using implicit differentiation.
2. Express the circle x2 + y2 = 34 in parametric equations and find the equation of the normal at the point (3, -5)
3. For the circle described by the parametric equations x = 2cos t + 1 and y = 2sin t − 5 find the equation of the tangent at the point where t = π / 4
4. For the circle described by the parametric equations x = 5cos t + 4 and y = 5sin t − 5 find the equation of the normal at the point where t = π / 3
5. Use the parametric method to find the equation of tangent to the ellipse 
at the point (2, 2)
6. Find the equation of the tangent to the ellipse described by x = 6cos t and y = 4sin t at the point where t = 3π/ 4.
7. Find the equation of the tangent to the hyperbola described by x = 4sec t and y = 2tan t at the point where t = π/ 4.
8. Find the equation of the normal to the hyperbola described by x = 6sec t and y = 4tan t at the point where t = 3π/ 4.
9. For the curve, defined parametrically by x = 5cos θ and y = 3sin θ:
a. Find the gradient of the tangent to the curve at (5cos θ, 3sin θ)
b. Show that the tangent to the curve at (5cos θ, 3sin θ) cuts the y-axis at 3/ sin θ
10. A curve has parametric equations x = -t 2 and y = 3 + t 3
a. Find the gradient of the curve at the point (-t 2 , 3 + t 3)
b. Find the equation of the tangent to the curve at the point where t = -1
c. This tangent cuts the curve at another point B. Find the coordinates of B.
