- #1

rajeshmarndi

- 319

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##a_1a_2x^2+(a_1b_2+b_1a_2)xy+b_1b_2y^2+(a_1c_2+c_1a_2)x+(b_1c_2+c_1b_2)y+c_1c_2=0##

i.e ##ax^2+2hxy+by^2+2gx+2fy+c=0##

Now if we take ##a_1=0##, then the first line becomes ##b_1y+c_1=0## i.e 1st line is parallel to x-axis . Then the pair of striaght line equation becomes ##2{h}'xy+by^2+2{g}'x+2fy+c=0##

In other words the coefficient of ##x^2## i.e ##a## becomes zero and still we have the pair of straight line equation.