Assertion :The point $(7, - 3)$ relative to hyperbola $9 x^{2} - 4 y^{2} = 36$ lies inside it. Reason: If the point $(x_{1}, y_{1})$ lies outside the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ then $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 > 0$ .

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Given hyperbola is,
$9 x^{2} - 4 y^{2} = 36 \Rightarrow \frac{x^{2}}{4} - \frac{y^{2}}{9} = 1$
Given point is $(7, - 3)$
$∴ \frac{49}{4} - \frac{9}{9} - 1 = \frac{41}{4} > 0 ∴$ Given point lies inside the hyperbola.
So Assertion (A) is true but Reason (R) is false.

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Assertion :The point (7,−3) relative to hyperbola 9x2−4y2=36 lies inside it. Reason: If the point (x1,y1) lies outside the hyperbola x2a2−y2b2=1 then x21a2−y21b2−1>0.

The correct option is C Assertion is correct but Reason is incorrectGiven hyperbola is,9x2−4y2=36⇒x24−y29=1 Given point is (7,−3)∴494−99−1=414>0∴ Given point lies inside the hyperbola. So Assertion (A) is true but Reason (R) is false.

Assertion :The point $(7, - 3)$ relative to hyperbola $9 x^{2} - 4 y^{2} = 36$ lies inside it. Reason: If the point $(x_{1}, y_{1})$ lies outside the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ then $\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 > 0$ .