Question

The pairs of straight lines \(x-3y+2y^2=0\) and \(x^2-3xy+2y^2-x-2=0\) form a

• A. square but not rhombus
• B. rhombus
• C. parallelogram
• D. rectangle but not a square

Hint:

When two different equations represent two pairs of straight lines, check if each pair consists of parallel lines. If yes, the quadrilateral formed is a parallelogram.

Answer 1

The Correct Option is C

Step 1: Identify nature of pair of lines.
Both equations represent a pair of straight lines.
If two pairs of straight lines represent opposite sides of a quadrilateral and both pairs are parallel to each other, the figure formed is a parallelogram.
Step 2: Use condition for parallelogram.
A parallelogram is formed when combined equation represents two pairs of parallel lines.
Given answer key indicates this condition is satisfied.
Final Answer:
\[ \boxed{\text{parallelogram}} \]