Question

The equation $x^2+k{y}^2+4xy=0$ represents two coincident lines, if $k=$

• A. $0$
• B. $1$
• C. $4$
• D. $16$

Answer 1

The correct option is C

$4$

Explanation for the correct option:

Find the value of $k$.

We know that, if a equation $A{x}^2+2Hxy+B{y}^2=0$ represent a pair of coincident lines, then $H^2-AB=0$.

A equation $x^2+k{y}^2+4xy=0$ of pair of coincident lines is given.

So,

$$\begin{gathered} 2^2-k=0 \\ \Rightarrow k=4 \end{gathered}$$

Therefore, the value of $k$ is equal to $4$.

Hence, the option $C$ is correct .