• # question_answer Statement-1: The straight line $2x+3y=4$ intersects the hyperbola $4{{x}^{2}}-9{{y}^{2}}=36$ in exactly one point. Statement-2: The line is parallel to an asymptote of the hyperbola. A)  Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.B)  Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.C)  Statement-1 is true, Statement-2 is false.D)  Statement-1 is false, Statement-2 is true.

The hyperbola is$\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{4}=1$. It's asymptotes are $y=\pm \frac{2}{3}x$. Clearly the given line is parallel to $y=-\frac{2}{3}x$, hence intersects the hyperbola at exactly one point.