Assertion :The point P $(4, - 3)$ lies outside the ellipse $5 x^{2} + 7 y^{2} = 140$ Reason: Let $S_{1} = 5 x^{2} + 7 y^{2} - 140$ and point P be $(4, - 3)$ then $S_{1} > 0$

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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Given equation is $5 x^{2} + 7 y^{2} = 140$
$\frac{x^{2}}{140 / 5} + \frac{y^{2}}{140 / 7} = 1 \frac{x^{2}}{28} + \frac{y^{2}}{20} = 1$
Substituting $(4, - 3)$ we get,
$\frac{16}{28} + \frac{9}{20} - 1 = \frac{4}{7} + \frac{9}{20} - 1 = \frac{143}{140} - 1 > 0$
It lies outside the ellipse as $S_{1} > 0$

Reason is the correct explanation for assertion.

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Similar questions

Q. Assertion :The point P

(1, - 3)

lies inside the ellipse

5 x^{2} + 7 y^{2} = 140

Reason: Let

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

and point P be

(1, - 3)

then

S_{1} > 0

Q. Assertion: The compressibility factor for

H_{2}

and

H e

(1 + \frac{P b}{R T})

Reason: The compressibility factor for

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Assertion: All the points (1, 0), (-1, 0), (2, 0) and (5, 0) lie on the x – axis.

Reason: Equation of the x – axis is y = 0
Now, choose the correct option.

Assertion – The non-fusible impurities present in iron ore are removed by $C a C O_{3}$ .

Reason: $C a C O_{3}$ which decomposes into $C a O$ and $C O_{2}$ . The $C a O$ formed reacts with $S i O_{2}$ to remove silica

Assertion (A) o-nitrophenol is less soluble in water than the m- and p-isomers.
Reason (R) m and p-nitrophenols exist as associated molecules.
(a) Assertion and reason both are correct and reason is correct explanation of assertion.
(b) Assertion and reason both are wrong statements.
(c) Assertion is correct statement but reason is wrong statement.
(d) Assertion is wrong statement but reason is correct statement.
(e) Both assertion and reason are correct statements but reason is not correct explanation of assertion.

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Assertion :The point P (4,−3) lies outside the ellipse 5x2+7y2=140 Reason: Let S1=5x2+7y2−140 and point P be (4,−3) then S1>0

Assertion :The point P $(4, - 3)$ lies outside the ellipse $5 x^{2} + 7 y^{2} = 140$ Reason: Let $S_{1} = 5 x^{2} + 7 y^{2} - 140$ and point P be $(4, - 3)$ then $S_{1} > 0$