Question

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) g² = ac

Answer 1

Correct option: (C) 2fgh = af² + ch² (D) g² = ac

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