MHT CET · Maths · Straight Lines
Two sides of a square are along the lines \(5 x-12 y+39=0\) and \(5 x-12 y+78=0\), then area of the square is
- A 9 sq. units.
- B \(\frac{1}{3}\) sq. units.
- C 18 sq. units.
- D 3 sq. units.
Answer & Solution
Correct Answer
(A) 9 sq. units.
Step-by-step Solution
Detailed explanation
Given equations of lines are \(5 x-12 y+39=0\) and \(5 x-12 y+78=0\).
Slope of \(5 x-12 y+39=0\) is \(\frac{5}{12}\)
Slope of \(5 x-12 y+78=0\) is \(\frac{5}{12}\)
\(\therefore \quad\) Lines are parallel.
\(\therefore \quad\) Distance between two parallel lines \(=\left|\frac{\mathrm{c}_1-\mathrm{c}_2}{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}\right|\)
\(\begin{aligned}
& =\left|\frac{39-78}{\sqrt{5^2+(-12)^2}}\right| \\
& =3 \text { units }
\end{aligned}\)
\(\therefore \quad\) Side of the square \(=3\) units
\(\therefore \quad\) Area of square \(=3^2=9\) sq. units
Slope of \(5 x-12 y+39=0\) is \(\frac{5}{12}\)
Slope of \(5 x-12 y+78=0\) is \(\frac{5}{12}\)
\(\therefore \quad\) Lines are parallel.
\(\therefore \quad\) Distance between two parallel lines \(=\left|\frac{\mathrm{c}_1-\mathrm{c}_2}{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}\right|\)
\(\begin{aligned}
& =\left|\frac{39-78}{\sqrt{5^2+(-12)^2}}\right| \\
& =3 \text { units }
\end{aligned}\)
\(\therefore \quad\) Side of the square \(=3\) units
\(\therefore \quad\) Area of square \(=3^2=9\) sq. units
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- A random variable X has p.m. f. \(\mathrm{P}(\mathrm{X}=x)=\frac{{ }^4 \mathrm{C}_x}{2^4}, x=0,1,2,3,4\) and \(\mu\) and \(\sigma^2\) are mean and variance respectively of random variable \(X\), thenMHT CET 2025 Medium
- \(\int_0^1|5 x-3| \mathrm{d} x=\)MHT CET 2022 Easy
- The value of \(m\), such that \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-m}{2}\) lies in the plane \(2 x-4 y+z=7\), isMHT CET 2024 Easy
- If one of the lines given by \(k x^2+x y-y^2=0\) bisect the angle between the co-ordinate axes, then the values of \(\mathrm{k}\) areMHT CET 2021 Medium
- A man and his wife appear for an interview for two posts. The probability of the husband's selection is \(\frac{1}{7}\). and that of the wife's selection is \(\frac{1}{5}\). If they appear for the interview independently, then the probability that only one of them is selected, isMHT CET 2024 Easy
- The distance between the lines given by \(3 x+4 \mathrm{y}=9\) and \(6 x+8 \mathrm{y}=15\) isMHT CET 2020 Easy
More PYQs from MHT CET
- Antipyretics are used toMHT CET 2009 Medium
- The particular solution of the differential equation \(\cos \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)=0.5, \mathrm{y}=1\) at \(x=0\) isMHT CET 2025 Medium
- A spherical conductor of diameter \(6 \mathrm{~mm}\) is kept in uniform electric field of intensity \(2 \times 10^7 \mathrm{~N} / \mathrm{C}\). The maximum charge on the conductor is
\(\left[\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right.\) SI units \(]\)MHT CET 2022 Easy - The central carbon atom of a free radical containsMHT CET 2011 Medium
- The motion of the particle is given by the equation \(x=A \sin \omega t+B \cos \omega t\).
The motion of the particle isMHT CET 2025 Easy - The phagocytic cells of liver are ________.MHT CET 2025 Hard