If in the general quadratic equation f(x, y) | vedclass

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Question

(A) The general quadratic equation $f(x, y) = ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if $\Delta = abc + 2fgh - af

Vedclass · Accepted Answer

Two parallel straight lines

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(A) The general quadratic equation $f(x, y) = ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines if $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.If $h^2 = ab$,the angle $	heta$ between the lines is given by $	an 	heta = \frac{2\sqrt{h^2 - ab}}{a + b}$.Since $h^2 = ab$,we have $	an 	heta = 0$,which implies $	heta = 0$.When $\Delta = 0$ and $h^2 = ab$,the lines are parallel.If $g^2 = ac$ and $f^2 = bc$ also hold,the lines are coincident; however,in the general case where only $\Delta = 0$ and $h^2 = ab$ are given,the lines are parallel.

If in the general quadratic equation $f(x, y) = ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$,$\Delta = 0$ and $h^2 = ab$,then the equation represents:

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