Let the equation of the circle, which touches x -axis at the point (a, 0), a > 0 and cuts off an intercept of length b on y -axis be x² + y² - α x + β y + γ = 0. If the circle lies below x -axis, then the ordered pair (2a, b²) is equal to

Coordinate Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q156

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

Let the equation of the circle, which touches

x

-axis at the point

(a, 0)

a > 0

and cuts off an intercept of length

b

y

-axis be

x^2 + y^2 - \alpha x + \beta y + \gamma = 0

. If the circle lies below

x

-axis, then the ordered pair

(2a, b^2)

is equal to