Circles
Circle
nta_abhyas_2025
Grade 11
Question:
Lines $L_1$ & $L_2$ are rotating in an anticlockwise direction about the points $A(-2, 0)$ and $B(2, 0)$ respectively in such a way that the speed of angle of rotation of $L_1$ with respect to $L_2$ is double. Initially equation of both lines are $y = 0$. If the angle of rotation of the $L_2$ varies between $0$ to $\frac{\pi}{2}$, then the locus of the point of intersection $P$ of lines $L_1$ & $L_2$ is part of a circle whose radius is equal to
2 units
4 units
6 units
8 units
Step-by-Step Solution
Key Concept: The equation of a circle with center $(h, k)$ and radius $r$ is $(x - h)^2 + (y - k)^2 = r^2$
Given that the locus of point $P$ is part of a circle with center at $(2, 0)$ and radius equal to 4 units. The question asks for the radius value. From the given information, the radius of the circle is directly stated as 4 units.
Correct Answer: 4