TS EAMCET · Maths · Pair of Lines
The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intersection of the lines \(x+2 y-3=0\) and \(2 x-y-1=0\) is
- A \((2 x-y-1+4 \sqrt{5})(x+2 y-3+4 \sqrt{5})=0\)
- B \((2 x-y-1-4 \sqrt{5})(x+2 y-4 \sqrt{5})=0\)
- C \((2 x-y-2 \sqrt{5})(x+2 y+2 \sqrt{5})=0\)
- D \((2 x-y-1-2 \sqrt{5})(x+2 y-3+2 \sqrt{5})=0\)
Answer & Solution
Correct Answer
(D) \((2 x-y-1-2 \sqrt{5})(x+2 y-3+2 \sqrt{5})=0\)
Step-by-step Solution
Detailed explanation
Since given lines are perpendicular and whose intersection point is \((1,1)\) Let possible pair of adjacent sides be \(\begin{aligned} & x+2 y+C_1=0 \text { and } 2 x-y+C_2=0 \\ & \therefore \frac{1+2+C_1}{\sqrt{5}}=2 \Rightarrow C_1=-3+2 \sqrt{5}\end{aligned}\) Now,…
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
- The value of \(\left\{x \in \mathbb{R} \mid\left[\log (1.6)^{1-x^2}-(0.625)^{6(1+x)}\right] \in \mathbb{R}\right\}\) isTS EAMCET 2013 Medium
- \(E_1: a+b+c=0, \quad\) if 1 is a root of \(a x^2+b x+c=0, \quad E_2: b^2-a^2=2 a c\), if \(\sin \theta\), \(\cos \theta\) are the roots of \(a x^2+b x+c=0\) Which of the following is true?TS EAMCET 2005 Medium
- If and are the roots of the quadratic equation thenTS EAMCET 2019 Easy
- If the product of the perpendicular distances from any point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) to its asymptotes is \(\frac{36}{13}\) and its eccentricity is \(\frac{\sqrt{13}}{3}\), then \(a-b=\)TS EAMCET 2025 Medium
- In a \(\triangle A B C\), if \(\cos A+\cos B+\cos C\) \(=a+b \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}\), then \((a+b)\) is equal toTS EAMCET 2021 Medium
- balls are drawn one after the other without replacement from an urn containing red, blue and yellow balls. The probability of getting three different coloured balls isTS EAMCET 2022 Medium
More PYQs from TS EAMCET
- For the equation \(x^4+x^3-4 x^2+x-1=0\) the ratio of the sum of the squares of all the roots to the product of the distinct roots isTS EAMCET 2020 Medium
- If the degree of dissociation of formic acid is \(11.0 \%\), the molar conductivity of 0.02 M solution of it is (Given, \(\lambda^{\circ}\left(\mathrm{H}^{+}\right)=349.6 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}, \lambda^{\circ}\left(\mathrm{HCOO}^{-}\right)=54.6\) \(\mathrm{S} \mathrm{cm}^2 \mathrm{~mol}^{-1}\) )TS EAMCET 2024 Hard
- If \((4,3)\) and \((1,-2)\) are the end points of a diagonal of a square, then the equation of one of its sides isTS EAMCET 2024 Easy
- Formic acid on heating with concentrated \(\mathrm{H}_2 \mathrm{SO}_4\) at 373 K gives X, a colourless substance and Y , a good reducing agent. The number of \(\sigma\) and \(\pi\) bonds in \(\mathrm{X}, \mathrm{Y}\) are respectivelyTS EAMCET 2024 Easy
- Identify all the species that do not exist \[ \mathrm{H}_2^{+}, \mathrm{He}_2^{2+}, \mathrm{Li}_2^{2-}, \mathrm{Ne}_2, \mathrm{Be}_2^{-}, \mathrm{He}_2 \]TS EAMCET 2022 Hard
- Match the following:
The correct answer is \(\begin{array}{llllllll}A & B & C & D & A & B & C & D\end{array}\)TS EAMCET 2019 Medium