| 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.
Correct Answer: A
Solution :
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.
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