Question

If the lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ intersect on the x-axis, which of the following is in general incorrect

• A. $abc = 2fgh$
• B. $g^2 = ac$
• C. $af^2 = ch^2$
• D. $af^2 + ch^2 = 2fgh$

Hint:

Familiarity with standard identities for conic sections helps identify incorrect general relations.

Answer 1

The Correct Option is A

If the pair of lines intersects on the x-axis, then the point of intersection lies on $y = 0$.
Substituting $y = 0$ in the general second degree equation: $ax^2 + 2gx + c = 0$
The rest of the expressions relate to conditions derived from combining coefficients.
Among the given, the equation $abc = 2fgh$ is not a standard identity and is generally incorrect.