Question

If two lines represented by the equation \(x^{2}+bcy^{2}=(b+c)xy\) are coincident, then ____

• A. \(b=c^{2}\)
• B. \(b^{2}=c\)
• C. \(b=c\)
• D. \(b=-c\)

Hint:

Factorise the equation and require the two lines to be the same.

Answer 1

The Correct Option is C

Step 1: Rewrite
\(x^{2}+bcy^{2}=(b+c)xy\) becomes \(x^{2}-(b+c)xy+bcy^{2}=0\).

Step 2: Factorise
\(x^{2}-bxy-cxy+bcy^{2}=(x-by)(x-cy)=0\). The lines are \(x=by\) and \(x=cy\).

Step 3: Coincide
The two lines are the same when \(b=c\), option (C).

Final Answer:
The lines coincide when \(b=c\). \[ \boxed{\text{(C) }b=c} \]