# The circle C : x² + y² = 3, with centre at O, intersects the parabola x² = 2 y

The circle C : x² + y² = 3, with centre at O, intersects the parabola x² = 2 y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2√3 and centres Q2 and Q3, respectively. If Q2 and Q3 lie on the y-axis, then-

- Q2Q3 = 12
- R2R3 = 4 √6
- area of the triangle OR2R3 is 6 √2
- area of the triangle PQ2Q3 is 4 √2

** Answer: **Q2Q3 = 12

R2R3 = 4 √6

area of the triangle OR2R3 is 6 √2