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 $(1+\text{i})(1+2\text{i})(1+3\text{i})...(1+\text{ni})=\text{a}+\text{ib},$ then $2\times5\times10\times...\times(1+\text{n}^2)$ is equal to:
→The locus of the centre of the circle which cuts off intercepts of length $2a$ and $2b$ from $x$ - axis and $y$ - axis respectively, is
→If the curves, $\frac{x^{2}}{a}+\frac{y^{2}}{b}=1$ and $\frac{x^{2}}{c}+\frac{y^{2}}{d}=1$ intersect each other at an angle of $90^{\circ},$ then which of the following relations is TRUE ?
→The variance $\sigma^2$ of the data is $ . . . . . .$
→| $x_i$ | $0$ | $1$ | $5$ | $6$ | $10$ | $12$ | $17$ |
| $f_i$ | $3$ | $2$ | $3$ | $2$ | $6$ | $3$ | $3$ |
If a point $(x,\;y) \equiv (\tan \theta + \sin \theta ,\;\tan \theta - \sin \theta )$, then locus of $(x, y)$ is
→Let $f:(0,1) \rightarrow \mathbb{R}$ be the functions defined as $f(x)=\sqrt{n}$ if $x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)$ where $n \in N$. Let $g:(0,1) \rightarrow \mathbb{R}$ be a function such that $\int_{x^2}^x \sqrt{\frac{1-t}{t}} d t$ $ < g(x) < 2 \sqrt{x}$ for all $x \in(0,1)$. Then $\lim _{x \rightarrow 0} f(x) g(x)$
→The quantity of $A$ and $B$ in one day for which profit will be maximum is:
→If $A + B + C = \pi \,(A,B,C > 0)$ and the angle $C$ is obtuse then
→The square root of $3 -4i$ is
→A garrison of $nn$ men had enough food to last for $30$ days. After $10$ days, $50$ more men joined them. If the food now lasted for $1616$ days, what is the value of $n?$
→