Cambridge Rectangular Hyperbola Q (1 Viewer)

[ordnaiv]

Hey guys, this is just question 9 from Exercise 3.4:

P(ct, c/t), where t=/= 1, lies on the rectangular hyperbola xy=c^2. The tangent and normal at P meet the line y=X at T and N respectively. Show that:

a) OP = PN
b) OT.ON =4c^2

I was just wondering if there was another way of doing this without using the distance formula because the algebra is really annoying - any help would be great thanks.

 

[jyu]

Hey guys, this is just question 9 from Exercise 3.4:

P(ct, c/t), where t=/= 1, lies on the rectangular hyperbola xy=c^2. The tangent and normal at P meet the line y=X at T and N respectively. Show that:

a) OP = PN
b) OT.ON =4c^2

I was just wondering if there was another way of doing this without using the distance formula because the algebra is really annoying - any help would be great thanks.

Use the gradient of PN, OP and y = x to show anglePON = anglePNO.