Question

Assertion :The point P $(1,-3)$ lies inside the ellipse $5x^2+7y^2=140$ Reason: Let $S=5x^2+7y^2-140$ and point P be $(1,-3)$ 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 C Assertion is correct but Reason is incorrect

Ellipse : ${5x}^2+{7y}^2=140$

putting point P(1,-3) in ellipse we get

$=5\times {\left(1\right)}^2+7\times {(-3)}^2-140$

$=5+63-140$

$=-72(<0)$

Hence, point lies inside ellipse

$S={5x}^2+{7y}^2-140$

P(1,-3)

$S_1>0$ (this implies point is outside ellipse, but its not)

Hence, Assertion is correct but reason is incorrect.