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0 votes
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in Mathematics by (70.7k points)

If the straight lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the x-axis then 

(A) ag = fh 

(B) ah = fg 

(C) 2fgh = af2 + ch2 

(D) None of these

1 Answer

+1 vote
by (71.5k points)
selected by
 
Best answer

Correct option (C)

Explanation:

ax2 + 2hxy + by2 + 2gx + 2fy + c = 0

put y = 0

⇒ ax2 + 2gx + c = 0

for D = 0, g2 = ac 

Now for straight line

abc + 2fgh – af2 – bg2 – ch2 = 0

Since g2 = ac

so 2fgh = af2 + ch2

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