Let C₁ be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C₂ be the circle with centre (1, 3) that touches C₁ externally at the point (α, β). If (β - α)² = m/n, gcd (m, n) = 1, then m + n is equal to:

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q184

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumCoordinate Geometry478× since 2002

Let

C_1

be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let

C_2

be the circle with centre

(1, 3)

that touches

C_1

externally at the point

(\alpha, \beta)

. If

(\beta - \alpha)^2 = \frac{m}{n}

\gcd(m, n) = 1

, then

m + n

is equal to: