Conic Sections

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point (2,5) and intersects the circle C at exactly two points. If the set of all possible values of r is the interval ( , ), then 3 -2 is equal to :

1. 10
2. 12
3. 14
4. 15

Let the parabola y=x2+px-3, meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1,-1) passes through the points P, Q and R, then the area of PQR is :

1. 4
2. 6
3. 5
4. 7

Let P(4,4 3) be a point on the parabola y2=4ax and PQ be a focal chord of the parabola. If M and N are the foot of perpendiculars drawn from P and Q respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :

1. 34 33
2. 343 38
3. 17 3
4. 263 38

Let E: x2a2+ y2b2=1, a>b and H: x2A2- y2B2=1. Let the distance between the foci of E and the foci of H be 2 3. If a-A=2, and the ratio of the eccentricities of E and H is 13, then the sum of the lengths of their latus rectums is equal to :

1. 10
2. 7
3. 9
4. 8