Assertion :Angle between the lines represented by $3 x^{2} + 10 x y + 3 y^{2} - 2 x + 2 y - 1 = 0$ and $3 x^{2} + 10 x y + 3 y^{2} - 11 x + 7 y - 20 = 0$ is same. Reason: Equations of the bisectors of the angles between the lines $3 x^{2} + 10 x y + 3 y^{2} = 0$ is $x^{2} - y^{2} = 0$

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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
ASSERTION:
Angle is same because one of the lines of first pair of lines is parallel to one of the lines of the second pair of lines and similarly the other lines of each pair are parallel.
REASON:
The equation of angular bisectors for the pair of straight lines $a x^{2} + 2 h x y + b y^{2} = 0$ is $h x^{2} - (a - b) x y - h y^{2}$
Here $a = 3, b = 3, h = 5$ .therefore the equation of angular bisectors is $5 x^{2} - (3 - 3) x y - 5 y^{2} = 0$
$\Rightarrow x^{2} - y^{2} = 0$

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Assertion :Angle between the lines represented by 3x2+10xy+3y2−2x+2y−1=0 and 3x2+10xy+3y2−11x+7y−20=0 is same. Reason: Equations of the bisectors of the angles between the lines 3x2+10xy+3y2=0 is x2−y2=0

Assertion :Angle between the lines represented by $3 x^{2} + 10 x y + 3 y^{2} - 2 x + 2 y - 1 = 0$ and $3 x^{2} + 10 x y + 3 y^{2} - 11 x + 7 y - 20 = 0$ is same. Reason: Equations of the bisectors of the angles between the lines $3 x^{2} + 10 x y + 3 y^{2} = 0$ is $x^{2} - y^{2} = 0$