Measurement Of Angles

Step 1: Compute derivatives
The slopes of the curves at the point of intersection determine

%5Ctan%20%5Ctheta

. 1st equation:

y%5E2%20%3D%20x

, differentiating:

2y%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%201%20%5CRightarrow%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2y%7D.

2nd equation:

x%5E2%20%2B%20y%5E2%20%3D%202

, differentiating:

2x%20%2B%202y%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%200%20%5CRightarrow%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%20-%5Cfrac%7Bx%7D%7By%7D.

Step 2: Compute $%5Ctan%20%5Ctheta$

%5Ctan%20%5Ctheta%20%3D%20%5Cleft%7C%20%5Cfrac%7Bm_1%20-%20m_2%7D%7B1%20%2B%20m_1%20m_2%7D%20%5Cright%7C.

Substituting slopes:

%5Ctan%20%5Ctheta%20%3D%20%5Cleft%7C%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2y%7D%20%2B%20%5Cfrac%7Bx%7D%7By%7D%7D%7B1%20-%20%5Cfrac%7Bx%7D%7B2y%7D%7D%20%5Cright%7C.

x%20%3D%201%2C%20y%20%3D%201

%5Ctan%20%5Ctheta%20%3D%20%5Cleft%7C%20%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%20%2B%201%7D%7B1%20-%20%5Cfrac%7B1%7D%7B2%7D%7D%20%5Cright%7C%20%3D%20%5Cleft%7C%20%5Cfrac%7B%5Cfrac%7B3%7D%7B2%7D%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5Cright%7C%20%3D%203.

Thus, the correct answer is

%5Cboxed%7B3%7D

Chapter Questions
1 MCQs