The parametric equations of a curve are x=#t^2# and y=#3/t#. Points P and Q with parameters p and q respectively lie on the curve. (pls see below). ?
(a) Find the gradient of chord PQ and deduce the gradient of the tangent to the curve at point P
(b) Find the coordinates of points A and B, when the tangent at P meets the x-axis and y-axis respectively.Show that area of triangle OAB is #9/2# P units.
(a) Find the gradient of chord PQ and deduce the gradient of the tangent to the curve at point P
(b) Find the coordinates of points A and B, when the tangent at P meets the x-axis and y-axis respectively.Show that area of triangle OAB is
1 Answer
The slope of the tangent at
Explanation:
Third degree; hyperbola-like in the first and fourth quadrants.
We have
The slope (aka gradient) between them is
The tangent slope is
The line through
We have x intercept
This is a right triangle because the sides are the axes. So the legs are the altitudes and bases. The area is
That's different than what the question said. Let's try it for
Tangent line:
x intercept
I think the question is wrong. I'll graph for
Plot
graph{ 0=(xy^2-9)(3 x + 2 y - 9) [-4.67, 15.33, -3.84, 6.16]}