Hi i have answered parts 1 and 2 of this question am stuck on part 3.
1 A curve has a parametric equations x=t^2 y=4t
Find the equation of the normal to this curve at (t^2,4t)
(i have solved this using parametric differentiation and getting the equation as tx+2y-8t-t^3 using y-y1=m(x-x1) we know that y=4t and x=t^2 and dy/dx is what we have solved using parametric differentiation)

2.find the coordinate of the points where the normal cuts the coordinates axes.
setting y=0 x= 8+t^2)

3.find in terms of t, the area of the triangle enclosed by the normal and the axes.(where am stuck)

Question

Hi i have answered parts 1 and 2 of this question am stuck on part 3.
1 A curve has a parametric equations x=t^2 y=4t
Find the equation of the normal to this curve at (t^2,4t)
(i have solved this using parametric differentiation and getting the equation as tx+2y-8t-t^3 using y-y1=m(x-x1) we know that y=4t and x=t^2 and dy/dx is what we have solved using parametric differentiation)

2.find the coordinate of the points where the normal cuts the coordinates axes.
setting y=0 x= 8+t^2)

3.find in terms of t, the area of the triangle enclosed by the normal and the axes.(where am stuck)

anonymous · Answer

the answer to part 3 should be (0,0.5t{8+t^2})