Let the sum of the focal distances of the point \(\mathrm{P}(4,3)\) on the hyperbola \(\mathrm{H}:\frac{{\mathrm{x}}^{2}}{{\mathrm{a}}^{2}}-\frac{{\mathrm{y}}^{2}}{{\mathrm{b}}^{2}}=1\) be \(8\sqrt{\frac{5}{3}}\). If for H , the length of the latus rectum is \(l\) and the product of the focal distances of the point \(P\) is \(m\) , then \(9{l}^{2}+6\mathrm{m}\) is equal to :-

[JEE Main 2025, 4 Apr (Shift 2)]

Question

Let the sum of the focal distances of the point \(\mathrm{P}(4,3)\) on the hyperbola \(\mathrm{H}:\frac{{\mathrm{x}}^{2}}{{\mathrm{a}}^{2}}-\frac{{\mathrm{y}}^{2}}{{\mathrm{b}}^{2}}=1\) be \(8\sqrt{\frac{5}{3}}\). If for H , the length of the latus rectum is \(l\) and the product of the focal distances of the point \(P\) is \(m\) , then \(9{l}^{2}+6\mathrm{m}\) is equal to :-

[JEE Main 2025, 4 Apr (Shift 2)]

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Let the sum of the focal distances of the point \(\mathrm{P}(4,3)\) on the hyperbola \(\mathrm{H}:\frac{{\mathrm{x}}^{2}…

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