Circles
Circle
star_batch_jee_advanced_2025
Grade 11
Question:
Let Q be a point from where tangents drawn to circle $g(x,y) = 0$ are mutually perpendicular. If A, B are the points of contact of tangent drawn from Q to circle $g(x,y) = 0$, then area of triangle QAB is:
Step-by-Step Solution
Key Concept: Concentric circles share the same center; the radius of $g$ is twice the radius of $f$.
Circle $f(x,y) = 0$ has center $(\frac{5}{2}, 2)$ and can be rewritten as $x^2 + y^2 - 5x - 4y + 4 = 0$. Circle $g(x,y) = 0$ is concentric with $f$ but has radius twice that of $f$, giving equation $x^2 + y^2 - 5x - 4y - \frac{59}{4} = 0$. The center of $f$ is at $(\frac{5}{2}, 2)$ with radius $\frac{3}{2}$, so $g$ has radius $3$.
Correct Answer: 4