The equation x^2 + k_1 y^2 + k_2 xy = 0 repre | vedclass

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Question

(A) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.For the lines to be perpendicular

Vedclass · Accepted Answer

$k_1 = -1$

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(A) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.For the lines to be perpendicular,the sum of the coefficients of $x^2$ and $y^2$ must be zero,i.e.,$a + b = 0$.Comparing the given equation $x^2 + k_2 xy + k_1 y^2 = 0$ with the general form,we have $a = 1$ and $b = k_1$.Applying the condition for perpendicularity:$1 + k_1 = 0$$\Rightarrow k_1 = -1$.Thus,the correct option is $A$.

The equation $x^2 + k_1 y^2 + k_2 xy = 0$ represents a pair of perpendicular lines,if

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