MCQ
The figure formed by the lines $\text{ax} \pm \text{by} \pm \text{c} = 0 $ is:
- Aa rectangle.
- Ba square.
- ✓a rhombus.
- DNone of these.
✓
Answer
Correct option: C.
a rhombus.
The given lines can be written separately in the following manner:
ax + by + c = 0 ...(1)
ax + by - c = 0 ...(2)
ax - by - c = 0 ...(3)
ax - by - c = 0 ...(4)
Graph of the given lines is given below:
Clearly, $\text{AB}=\text{BC}=\text{CD}=\text{DA}=\sqrt{\frac{\text{a}^2}{\text{c}^2}+\frac{\text{b}^2}{\text{c}^2}}=\frac{\sqrt{\text{a}^2+\text{b}^2}}{|\text{c}|}$
Thus, the region formed by the given lines is ABCD, which is a rhombus.
ax + by + c = 0 ...(1)
ax + by - c = 0 ...(2)
ax - by - c = 0 ...(3)
ax - by - c = 0 ...(4)
Graph of the given lines is given below:
Clearly, $\text{AB}=\text{BC}=\text{CD}=\text{DA}=\sqrt{\frac{\text{a}^2}{\text{c}^2}+\frac{\text{b}^2}{\text{c}^2}}=\frac{\sqrt{\text{a}^2+\text{b}^2}}{|\text{c}|}$
Thus, the region formed by the given lines is ABCD, which is a rhombus.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $\tan\text{A}=\frac{1}{2},\tan\text{B}=\frac{1}{3},$ then $\tan(2\text{A + B})$ is equal to:
→Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is
Let $A B C$ be a triangle with $\angle B=90^{\circ}$. Let $A D$ be the bisector of $\angle A$ with $D$ on $B C$. Suppose $A C=6 cm$ and the area of the $\triangle A D C$ is $10 cm ^2$. Then, the length of $B D$ in $cm$ is equal to
→The value of $ 2^\text{n}\big[1·3· 5…(2\text{n}-3)2\text{n}-1\big)$ is:
→The number of ways in which $5$ boys and $3$ girls can be seated in a row so that each girl in between two boys
→The centroid of triangle $A(3, 4, 5), B(6, 7, 2), C(0, -5, 2)$ is:
→The coefficient of $x^5$ in the expansion of $(1 + x^2)^5 (1 + x)^4$ is?
→For any two events A and B, which of the following is true?
If $\lim \limits_{x \rightarrow 0}\left\{\frac{1}{x^{8}}\left(1-\cos \frac{x^{2}}{2}-\cos \frac{x^{2}}{4}+\cos \frac{x^{2}}{2} \cos \frac{x^{2}}{4}\right)\right\}=2^{-k}$ then the value of $k$ is
→If $^{(\text{a}^2-\text{a})}\text{C}_{\text{2}}=^{(\text{a}^2-\text{a})\text{}}\text{C}_{\text{4}},$ is then x:
→