Let y² = 12x be the parabola and S be its focus. Let PQ be a focal chord of the parabola such that (SP)(SQ) = 147/4. Let C be the circle described taking PQ as a diameter. If the equation of a circle C is 64x² + 64y² - α x - 64√(3)y = β, then β - α is equal to:

Unclassified (maths): JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q149

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumUnclassified (maths)

Let

y^2 = 12x

be the parabola and

S

be its focus. Let

PQ

be a focal chord of the parabola such that

(SP)(SQ) = \frac{147}{4}

. Let

C

be the circle described taking

PQ

as a diameter. If the equation of a circle

C

64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta

, then

\beta - \alpha

is equal to:

Your answerInteger or decimal