Assertion (A): The lines 2x^2 + 5xy + 2y^2 = | vedclass

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(C) The given pair of lines is $2x^2 + 5xy + 2y^2 = 0$.Factoring the expression: $2x^2 + 4xy + xy + 2y^2 = 0$ $\Rightarrow 2x(x + 2y) + y(x + 2y) = 0$

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$(A)$ is true,$(R)$ is true,but $(R)$ is not the correct explanation for $(A)$

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(C) The given pair of lines is $2x^2 + 5xy + 2y^2 = 0$.Factoring the expression: $2x^2 + 4xy + xy + 2y^2 = 0$ $\Rightarrow 2x(x + 2y) + y(x + 2y) = 0$ $\Rightarrow (2x + y)(x + 2y) = 0$.The lines are $L_1: 2x + y = 0$ and $L_2: x + 2y = 0$.The slopes are $m_1 = -2$ and $m_2 = -\frac{1}{2}$.The third line is $L_3: x - 2y + 1 = 0$,which has slope $m_3 = \frac{1}{2}$.Since $m_1 	imes m_3 = (-2) 	imes (\frac{1}{2}) = -1$,lines $L_1$ and $L_3$ are perpendicular. Thus,they form a right-angled triangle. Assertion $(A)$ is true.The condition for $ax^2 + 2hxy + by^2 = 0$ to represent perpendicular lines is $a + b = 0$. Reason $(R)$ is true.However,$(R)$ describes the condition for the pair of lines represented by the quadratic equation to be perpendicular to each other,not the condition for forming a right-angled triangle with a third line. Thus,$(R)$ is not the correct explanation for $(A)$.

Assertion $(A)$: The lines $2x^2 + 5xy + 2y^2 = 0$ and $x - 2y + 1 = 0$ form a right-angled triangle.
Reason $(R)$: The equation $ax^2 + 2hxy + by^2 = 0$ represents a pair of perpendicular lines if $a + b = 0$.
Choose the correct answer.

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Assertion $(A)$: The lines $2x^2 + 5xy + 2y^2 = 0$ and $x - 2y + 1 = 0$ form a right-angled triangle.Reason $(R)$: The equation $ax^2 + 2hxy + by^2 = 0$ represents a pair of perpendicular lines if $a + b = 0$.Choose the correct answer.