A curve is given by the parametric equations x=t,y=#1/t#. (pls see details below). ?
(a) Find the equation of line passing through the points (s,#1/s# ) and (t,#1/t# ).
(b) Deduce the equation of tangent to the curve at the point (t,#1/t# ).
(c)Find the equation of normal to the curve at the point (t,#1/t# ).
If this normal cuts the curve again, find the coordinates of point of intersection
(a) Find the equation of line passing through the points (s,
(b) Deduce the equation of tangent to the curve at the point (t,
(c)Find the equation of normal to the curve at the point (t,
If this normal cuts the curve again, find the coordinates of point of intersection
1 Answer
Line through...:
Tangent:
Normal:
Other intersection:
Explanation:
Fun. We have
The line through
Multiplying both sides by
We get the tangent line as
For the normal line we swap the coefficients on
We plug in
Multiply by
We know
Let's plot these at
Plot
graph{0=(y-1/x)(x +2^2 y - 2(2))(2^3 x - 2 y - (2^4 -1))( (x- (-1/2^3) )^2+(y - (-2)^3)^2-.2^2) [-20, 20, -10, 10]}