Thread: Parametric Question

Hi

P(2ap, ap^2), Q(2aq,aq^2) and R(2ar,ar^2) are points on the parabola x^2 = 4ay.
a) Show that the equation of the normal at P is py+x = 2ap + ap^3.
b) Find the coordinates of the point of intersection of the normals at P and Q.

c) If the normals P,Q and R are constant, show that p +q +r=0.

How on earth do you do this??

Please help?

Originally Posted by xwrathbringerx

Hi

P(2ap, ap^2), Q(2aq,aq^2) and R(2ar,ar^2) are points on the parabola x^2 = 4ay.
a) Show that the equation of the normal at P is py+x = 2ap + ap^3.
b) Find the coordinates of the point of intersection of the normals at P and Q.

c) If the normals P,Q and R are constant, show that p +q +r=0.

How on earth do you do this??

Please help?

hi

(a) Use the chain rule to get the gradient of tangent , then use m1m2=-1 for the gradient of normal





so

gradient of normal=-1/p

Equation :

Now simplify

(b) Since Q is also a point on the parabola , its equation of normal would be , just swap the 'p' with 'q' , then have them equal to solve for the point of intersection .