A curve is defined by the parametric equations x = tē and y = 2t + 1
Find the equation of the tangent at the point where t = 2.
Let the equation of the tangent at the required point be:Originally Posted by Kiwigirl
We need to find the slope of the tangent, which is , and
to find this we need to use the result that:
So at the slope of the tangent is .
So now we know that the equation of the tangent is of the form:
and that at , and , so the tangent passes through the point
and the equation of the tangent is:
Hello,Originally Posted by Kiwigirl
as you may know the derivation of parametric(?) functions is done with
So you need the coordinates of the tangent point, which is (4, 5) and the slope, which you calculate with the formula given above:
. With t = 2 you get a slope of 1/2.
Now use the point slope formula of a line: