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Question

Find the value of k, if the following equations represent a pair of lines $$3{x^2} - 10xy + 3{y^2} + 16y + k = 0$$


Solution

compare the equation with $$ax^2+2hxy+by^2+2gx+2fy+c=0$$
$$a=3$$,$$b=3$$,$$h=-5$$,$$g=0$$,$$f=8$$,$$c=k$$
if $$abc+2fgh-af^2-bg^2-ch^2=0$$ then this equation represents a pair of straight lines
$$9k-192-25k=0$$
$$k=-12$$

Maths

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