AP EAMCET · Maths · Straight Lines
The triangle formed by \(x^2-4 x y+y^2=0\) and \(x+y+4 \sqrt{6}=0\) is
- A an equilateral triangle
- B a right angled triangle
- C an isosceles triangle
- D a scalene triangle
Answer & Solution
Correct Answer
(A) an equilateral triangle
Step-by-step Solution
Detailed explanation
\(x^2-4 x y+y^2=0\) \(\Rightarrow y^2-2 \cdot 2 x y+4 x^2=3 x^2\) \(\begin{array}{ll}\Rightarrow & (y-2 x)^2=3 x^2 \\ \Rightarrow & y-2 x= \pm \sqrt{3} x\end{array}\) \(y=(2 \pm \sqrt{3}) x\) \(\therefore\) The given triangle is an equilateral triangle.
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 equation of the circle passing through the points of intersection of the circles \(x^2+y^2+4 x+6 y-12=0\) and \(x^2+y^2-6 x-4 y-12=0\) and cutting the circle \(x^2+y^2-4 x+4 y+8=0\) orthogonally isAP EAMCET 2018 Medium
- If \(A\) and \(B\) are two events of a random experiment such that \(P(A)=0.6, P(B)=0.3\) and \(P(A \mid B)=0.5\) then \(P(\bar{B} \mid \bar{A})=\)AP EAMCET 2017 Easy
- If \(\mathrm{t}_{\mathrm{n}}=\frac{1}{4}(\mathrm{n}+2)(\mathrm{n}+3), \mathrm{n} \in \mathrm{N}\), then which one of the following is true?
Assertion (A) : \(\frac{1}{t_1}+\frac{1}{t_2}+\ldots+\frac{1}{t_{2003}}=\frac{2003}{3009}\)
Reason (R) : \(\frac{1}{\mathrm{t}_1}+\frac{1}{\mathrm{t}_2}+\ldots+\frac{1}{\mathrm{t}_{\mathrm{n}}}=\frac{4 \mathrm{n}}{(2 \mathrm{n}+3)}\)AP EAMCET 2025 Medium - In an ellipse, two vertices are \((5,0)\) and \((0,-4)\). Then the equation of the ellipse isAP EAMCET 2020 Easy
- If \(\tan A+\tan B=x\) and \(\cot A+\cot B=y\), then \(\tan (\mathrm{A}+\mathrm{B})=\)AP EAMCET 2023 Medium
- If the power of the point with respect to the circle is then equalsAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- The conductivity of \(0.001 \mathrm{M}\) acetic acid at a certain temperature is \(5.07 \times 10^{-5} \mathrm{~S} \mathrm{~cm}^{-1}\). If \(\wedge_m^0\) of acetic acid at the same temperature is \(390 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\), the dissociation constant of acetic acid at that temperature is:AP EAMCET 2017 Medium
- The distance between the origin and the normal to the curve drawn at is_____ unitsAP EAMCET 2021 Medium
- \(\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right) \ldots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}}=\)AP EAMCET 2018 Hard
- A person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score \(X\) is observed, then the range of \(x\) isAP EAMCET 2004 Hard
- Steam distillation process cannot be used for purifying which of the following?AP EAMCET 2020 Medium
- The polydispersity index of a polymer containing 10 molecules with molecular mass \(1.0 \times 10^4\) and 10 molecules with molecular mass \(1.0 \times 10^5\) is approximately.AP EAMCET 2018 Easy