| 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 |
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:
If \( x^2 = -16y \) is an equation of a parabola, then:
(A) Directrix is \( y = 4 \)
(B) Directrix is \( x = 4 \)
(C) Co-ordinates of focus are \( (0, -4) \)
(D) Co-ordinates of focus are \( (-4, 0) \)
(E) Length of latus rectum is 16
Let the focal chord PQ of the parabola $ y^2 = 4x $ make an angle of $ 60^\circ $ with the positive x-axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, $ S $ being the focus of the parabola, touches the y-axis at the point $ (0, \alpha) $, then $ 5\alpha^2 $ is equal to:
Find the next two terms of the series:
The given series is: \( A, C, F, J, ? \).
(A) O
(B) U
(C) R
(D) V
Choose the correct answer from the options given below: