Question

Assertion :The point P $(3,-4)$ lies outside the hyperbola $9x^2-y^2=1$ Reason: Let $S=9x^2-y^2-1$ and point P be $(3,-4)$ , then $S_1<0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is D Both Assertion and Reason are incorrect

If the point $(x_1,y_1)$ lies outside, on or inside the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ then $\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1<,=$ or $>0$.

Assertion- When we put P in the given hyperbola $S_1=127>0$ so $P(3,-4)$ lies inside, so given statement is incorrect

Reason- Reason is also incorrect because $S_1=127>0$