Question

Statement-l : The point $(7,-3)$ lies inside the hyperbola $9x^2-4y^2=36$ where as the point $(2,7)$ lies outside this.
Statement-2: The point $(x_1,y_1)$ lies outside, on or inside the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ according as $\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1<or=or>0$

• A. A) Statement - 1 is True, Statement - 2 is True; Statement -2 is a correct explanation for Statement - 1
• B. B) Statement - 1 is True, Statement - 2 is True; Statement -2 is NOT a correct explanation for Statement - 1
• C. C) Statement - 1 is True, Statement-2 is False
• D. D) Statement - 1 is False, Statement-2 is True

Answer 1

The correct option is A A) Statement - 1 is True, Statement - 2 is True; Statement -2 is a correct explanation for Statement - 1

Let $S\equiv 9x^2-4y^2-36=0$
Now at $(7,3),S=9(7{)}^2-4(3{)}^2-36=222>0$
and at $(2,7),S=9(2{)}^2-4(7{)}^2-36=-196<0$
Thus $(7,3)$ lie inside and $(2,7)$ outside the hyperbola
Hence both Assertion and Reason are correct and Assertion is followed by Reason.