If the points of intersection of two distinct conics x^2+y^2=4b and (a second conic, not p…

Question

If the points of intersection of two distinct conics $x^2+y^2=4b$ and (a second conic, not preserved in the source) lie on the curve $y^2=3x^2$, then $3\sqrt3$ times the area of the rectangle formed by the intersection points is \_\_\_\_\_\_\_\_.

Answer: 432

Accepted Answer

*(The second conic's equation is missing from the source, so $b$ cannot be independently pinned down --- using only $x^2+y^2=4b$ and $y^2=3x^2$, the intersection points are $(\pm\sqrt b,\pm\sqrt{3b})$, giving rectangle area $4\sqrt3\,b$, so $3\sqrt3	imes	ext{Area}=36b$; matching the given answer requires $b=12$. The stated answer is $432$.)*

Solutions · 1