(a) Use the identity for tan(x – y) (see Equation 14b in Appendix D) to show that if two lines L1, and L2 intersect at an angle α, then
where m1, and m2 are the slopes of L1 and L2 respectively.
(b) The angle between the curves C1 and C2 at a point of intersection P is defined to be the angle between the tangent lines to C1, and C2 at P (if these tangent lines exist). Use part (a) to find, correct to the nearest degree, the angle between each pair or curves at each point of intersection.
(i) y = x2 and y = (x – 2)2
(ii) x2 – y2 = 3 and x2 – 4x + y2 + 3 = 0
To show: If two lines intersect at an angle then .
Two lines are .
The slope of the lines are respectively.
Let be an inclination angle of the line respectively.
Here, the slopes of the line are .
The angle between two lines are
To find: The angle between each pair of curves at each points.
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