Circles
Circle
star_batch_jee_advanced_2025
Grade None
Question:
The equation(s) of the tangent at the point $(0, 0)$ to the circle, making intercepts of lengths $2a$ and $2b$ units on the coordinates axes, is(are):
ax + by = 0
ax - by = 0
x - y = 0
bx + ay = 0
Step-by-Step Solution
Key Concept: The tangent from the origin to a circle with center $(a, b)$ has equation $ax + by = 0$, derived from the condition that the line passes through the origin and is perpendicular to the radius.
The equation of a circle $(x + a^2) + (y + b)^2 = a^2 + b^2$ simplifies to $x^2 + y^2 + 2ax + 2by = 0$ or $x^2 + y^2 + 2bx + 2ay = 0$. The equation of the tangent from the origin is found by setting the tangent condition $ax + by = 0$ or $bx + ay = 0$, representing the chord of contact from the origin to the circle.
Correct Answer: 1,2,4