AP EAMCET · Maths · Pair of Lines
The lines \(a x^2+2 h x y+b y^2=0\) are at right angles if
- A \(a+b=0\)
- B \(a+b=1\)
- C \(h^2-a b=0\)
- D \(a=b\)
Answer & Solution
Correct Answer
(A) \(a+b=0\)
Step-by-step Solution
Detailed explanation
The acute angle \((\theta)\) between lines represented by equation \(a x^2+2 h x y+b y^2=0\), is \(\theta=\tan ^{-1}\left(\frac{2 \sqrt{h^2-a b}}{|a+b|}\right)\) If lines are perpendicular then \(a+b=0\).
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
- Consider the point \(P(\alpha, \beta)\) on the line \(2 x+y=1\). If the \(P\) and \((3,2)\) are conjugate points with respect to the circle \(x^2+y^2=4\), then \(\alpha+\beta=\)AP EAMCET 2024 Easy
- The area (in sq. units) of the region bounded by the curves \(y=x \log x\) and \(y=2 x-2 x^2\) isAP EAMCET 2018 Easy
- \(\lim _{x \rightarrow \infty} \frac{1^{77}+2^{77}+\ldots+n^{77}}{n^{78}}=\)AP EAMCET 2024 Easy
- If \(\lim _{x \rightarrow \infty} y(x)=\frac{\pi}{2}\), then the solution of \(x^3 \sin y \frac{d y}{d x}=2\) is \(\cos y=\)AP EAMCET 2023 Medium
- If \(f(x)=\sin x+\cos x\), then \(f\left(\frac{\pi}{4}\right) f^{(i v)}\left(\frac{\pi}{4}\right)\) is equal toAP EAMCET 2010 Easy
- Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}-2 \hat{k}, \vec{c}=\hat{i}-2 \hat{j}+3 \hat{k}\) and \(\overrightarrow{\mathrm{d}}=-4 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{d}}=x(\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}})-\frac{7}{9}(\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}})+\mathrm{z}(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})\), then \(x=\)AP EAMCET 2023 Easy
More PYQs from AP EAMCET
- In which of the following, complex ions are not in correct order with respect to their magnitude of crystal field splitting ?AP EAMCET 2025 Medium
- The system of equations \(x+2 y=3\) and \(3 x+6 y=a-2\) has no solutionAP EAMCET 2021 Easy
- Consider two liquids \(\mathrm{A}\) and \(\mathrm{B}\) in a U-shaped tube in static equilibrium as shown in the figure. If the density of the liquid \(A\) is twice the density of liquid \(B\), then the relation between \(h_A\) and \(h_B\) is
AP EAMCET 2022 Hard - Assertion (A)
The first ionisation energy of Be is greater than that of \(\mathrm{B}\).
Reason (R) \(2 p\) orbital has lower energy than \(2 s\) orbital.AP EAMCET 2021 Easy - Two points and with co-ordinates and are given respectively. Then, the locus of a point so that the area of is 9 sq.units is given by _____AP EAMCET 2020 Medium
- Which of the following conclusions could not be derived from Rutherford's -particle scattering experiment:AP EAMCET 2020 Easy