| LIST I | LIST II | ||
| A. | The angle between the straight lines, 2x2+ 3y2-7xy=0 is | I. | \(\tan^{-1}\frac{3}{5}\) |
| B. | The circles x2+y2+x+y=0 and x2+y2 +x-y=0 intersect at angle | II. | 25π |
| C. | The area of circle centered at (1,2) and passing through (4,6) is | III. | π/4 |
| D. | The parabola y2=4x and x2 =32y intersect at point (16,8) at angle | IV. | π/2 |
Two parabolas have the same focus $(4, 3)$ and their directrices are the $x$-axis and the $y$-axis, respectively. If these parabolas intersect at the points $A$ and $B$, then $(AB)^2$ is equal to:
Let \( y^2 = 12x \) be the parabola and \( S \) its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ) = \frac{147}{4} \). Let \( C \) be the circle described by taking \( PQ \) as a diameter. If the equation of the circle \( C \) is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then \( \beta - \alpha \) is equal to:


