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 $\text{ABCD,}$ 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 $\text{ABCD,}$ 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 $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5},$ then
→$(A)$ $\tan ^2 x=\frac{2}{3}$ $(B)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{1}{125}$
$(C)$ $\tan ^2 x=\frac{1}{3}$ $(D)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{2}{125}$
If $\sin \beta $ is the geometric mean between $\sin \alpha $ and $\cos \alpha ,$ then $\cos 2\beta $ is equal to
→Let $A = \{1, 2, 3, 4, 5\}; B = \{2, 3, 6, 7\}$. Then the number of elements in $(A × B) \cap (B × A)$ is
→In a city, the total income of all people with salary below $₹ 10000$ per annum is less than the total income of all people with salary above $₹ 10000$ per annum. If the salaries of people in the first group increases by $5 \%$ and the salaries of people in the second group decreases by $5 \%$, then the average income of all people
→The line $lx + my + n = 0$ will touch the parabola ${y^2} = 4ax$, if
→A pack of cards contains $4$ aces, $4$ kings, $4$ queens and $4$ jacks. Two cards are drawn at random. The probability that at least one of these is an ace, is
→If the two lines with slope $m_1$ and $m_2$ are perpendicular then their slopes has relation:
→In any discrete series (when all values are not same) the relationship between $M.D.$ about mean and $S.D.$ is
→The number of integers $n$ for which $3 x^3-25 x+n=0$ has three real roots is
→The number of straight lines that can be formed by joining $20$ points no three of which are in the same straight line except $4$ of them which are in the same line
→