Question

Find the equations of the tangents to the hyperbola
3x^2 - 4y^2 = 12, which are inclined at an angle 60° to X axis ? ( using Calculus)​

Answer 1

Step-by-step explanation:

$\tt \huge\color{blue}Solution: -$

$\tt \frac{ {3x}^{2} }{12} - \frac{ {4y}^{2} }{12} = \frac{12}{12} \\ \\ \\ \tt \frac{ {x}^{2} }{4} - \frac{ {4}^{2} }{3} = 1 \\ \\ \\ \tt \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {4}^{2} }{3} = 1 \\ \\ \\ \tt \: \: \: \: \: \: \: \: \: {a}^{2} = 4 \\ \\ \\ \tt \: \: \: \: \: \: \: \: \: {b}^{2} = 3 \\ \\ \\ \boxed{\tt equation \: \: of \: \: langent \: \: to \: \: hyperbola} \\ \\ \\ \tt y = mx ± \sqrt{ {a}^{2} {m}^{2} - {b}^{2} } \\ \\ \\ \\ \tt m = tan \: 60° \\ \\ \\ \tt : \implies \sqrt{3} \\ \\ \\ \tt y = \sqrt{3x} ± \sqrt{3x4 - 3} \\ \\ \\ \tt y = \sqrt{3x} ± \sqrt{9} \\ \\ \\ \tt y = \sqrt{3x} ± 3$