For ell in R,the equation (2 ell-3) x^2+2 ell | vedclass

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(D) The general equation of a pair of lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$. Comparing this with $(2\ell-3)x^2 + 2\ell

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for all values of $\ell \in R-[-3,1]$

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(D) The general equation of a pair of lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$. Comparing this with $(2\ell-3)x^2 + 2\ell xy - y^2 = 0$,we have $a = 2\ell-3$,$h = \ell$,and $b = -1$. For the equation to represent a pair of distinct lines,the condition $h^2 - ab > 0$ must be satisfied. Substituting the values: $\ell^2 - (2\ell-3)(-1) > 0$. $\ell^2 + 2\ell - 3 > 0$. Factoring the quadratic: $(\ell+3)(\ell-1) > 0$. This inequality holds when $\ell  1$. Thus,the condition is satisfied for all values of $\ell \in R - [-3, 1]$.

For $\ell \in R$,the equation $(2 \ell-3) x^2+2 \ell xy-y^2=0$ represents a pair of distinct lines

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