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Analytical Geometry> If the pairs of line represented by the e...

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If the pairs of line represented by the equation (ax^2+2hxy+by^2+2gx+2fy+c=0) intersect each other on y axis which is not origin then which of following is/are true
(a) g^2=ac
(b) f^2=bc
(c) 2fgh=bg^2+ch^2
(d) hc=gf

Adarsh Srivastav , 8 Years ago

Grade 11

1 Answers

Nishant Vora

Last Activity: 8 Years ago

the condition for this eqn to be a pair of sl is
…...............(1)
now both the straight line is intersecting on y axis
so x= 0

Put x= 0 in $ax^2+2hxy+by^2+2gx+2fy+c=0$

so $by^2 +2fy+c=0$

Now for this Quadratic y1 = y2 as there is a unique point

So D=0

So $4f^2 - 4bc = 0$

Hence, $f^2 - bc = 0$

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