Aspire Faculty ID #18088 · Topic: JEE Main 2026 (28 January Morning Shift) · Just now
JEE Main 2026 (28 January Morning Shift)

Let $ y = x $ be the equation of a chord of the circle $ C_1 $ (in the closed half-plane $ x \ge 0 $) of diameter 10 passing through the origin. Let $ C_2 $ be another circle described on the given chord as its diameter. If the equation of the chord of the circle $ C_2 $, which passes through the point $ (2, 3) $ and is farthest from the center of $ C_2 $, is $ x + ay + b = 0 $, then $ a - b $ is equal to

Solution



Equation of circle $ C_2 $ is

$ x^2 + y^2 - 5x - 5y = 0 $

its centre is $ \left( \frac{5}{2}, \frac{5}{2} \right) $

$ m_{AB} = -1 $

$ \therefore $ slope of required chord $ = 1 $

$ \therefore $ equation of required chord is $ x - y + 1 = 0 $

$ \therefore a = -1,; b = 2 $

$ \therefore a - b = -2 $

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