Question

In a general quadratic equation, if $f(x,y)=0,∆=0\text{and}{h}^2=ab,$then the equation represents

• A. Two parallel straight lines
• B. Two perpendicular straight lines
• C. Two intersecting lines
• D. None of these

Answer 1

The correct option is A

Two parallel straight lines

Explanation for the correct option:

Finding the orientation of lines with respect to the equation:

Given that,

$f(x,y)=0$

$∆=0$

It represents a pair of straight lines.

Let's find the orientation of lines with respect to each other.

$h^2=ab\left[\text{Given}\right]$

The angle between the pair of straight lines is given by:

$$\begin{gathered} \tan \left(\theta \right)=\frac{2\sqrt{h^2-ab}}{a+b} \\ \Rightarrow \tan \left(\theta \right)=\frac{2\sqrt{ab-ab}}{a+b} \\ \Rightarrow \tan \left(\theta \right)=0 \end{gathered}$$

Since the angle between the pair of lines is zero, the lines are parallel to each other.

Therefore, the equation represents two straight lines that are parallel to each other.

Hence, Option (A) is correct.