Let $ S $ denote the locus of the point of intersection of the pair of lines $$ 4x - 3y = 12\alpha,\quad 4\alpha x + 3\alpha y = 12, $$ where $ \alpha $ varies over the set of non-zero real numbers. Let $ T $ be the tangent to $ S $ passing through the points $ (p, 0) $ and $ (0, q) $, $ q > 0 $, and parallel to the line $ 4x - \frac{3}{\sqrt{2}} y = 0 $.
Then the value of $ pq $ is
Hydrogen peroxide is a chemical element including hydrogen and oxygen. Anhydrous hydrogen peroxide is a colorless, sugary liquid that breaks down quickly into oxygen and water. The chemical formula for hydrogen peroxide [H2O2] is H—O—O—H, here, each dash represents a single covalent link. Especially, each bond has a pair of mutual electrons, one from each of the atoms at the bond’s ends. The polar bonds are H—O bonds, but this is not the polar one - O—O bonds.