The reaction involved is an aldol condensation reaction. The mechanism is as follows:
The product is formed by the reaction of two molecules of benzaldehyde (PhCHO) and one molecule of acetone (CH$_3$COCH$_3$) in the presence of alkali and heat.
The reaction involves the removal of water (H$_2$O) through dehydration, leading to the formation of a conjugated system.
The major product contains:
-3 double bonds in the benzene ring (Ph),
-2 double bonds formed during the aldol reaction,
-carbonyl (C = O) group in the product.
Total $\pi$-bonds = 9.
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to: