AP EAMCET · Maths · Pair of Lines
If the co-ordinate axes are the bisectors of the angles between the pair of lines \(a x^2+2 h x y+b y^2=0\) where \(h^2>a b\) and \(a \neq b\), then
- A \(a+b=0\)
- B \(h=0\)
- C \(h \neq 0, a+b=0\)
- D \(a+b \neq 0\)
Answer & Solution
Correct Answer
(B) \(h=0\)
Step-by-step Solution
Detailed explanation
Equation of pair of bisectors of \[ \begin{aligned} & a x^2+2 h x y+b y^2=0 \text { is } \frac{x^2-y^2}{a-b}=\frac{x y}{h} \\ & \text { if } \quad h=0, x y=0 \\ & \Rightarrow \quad x=0, y=0 \end{aligned} \] Which are the equations of coordinate axes.
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
- Assertion (A): \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{(\sin x)^{\sqrt{2}} d x}{(\sin x)^{\sqrt{2}}+(\cos x)^{\sqrt{2}}}=\frac{\pi}{12}\)
Reason (R): \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{f(x) d x}{f(x)+f\left(\frac{\pi}{2}-x\right)}=\frac{\pi}{12}\)AP EAMCET 2023 Medium - \(\mathrm{P}\) is a point of intersection of the circles \(\mathrm{S} \equiv \mathrm{x}^2+\mathrm{y}^2-6 \mathrm{x}\) \(+2 k y+1=0\) and \(S^1 \equiv x^2+y^2+2 k x-6 y-7=0\). If the tangent at \(P\) to \(S=0\) pass through the centre of \(S^1=0\) and the tangent at \(\mathrm{P}\) to \(\mathrm{S}^1=0\) pass through the centre of \(\mathrm{S}=0\), then the radius of \(\mathrm{S}^1=0\) isAP EAMCET 2023 Medium
- The locus of the mid points of the chords of the hyperbola \(x^2-y^2=a^2\) which touch the parabola \(y^2=4 a x\) isAP EAMCET 2024 Medium
- If the chord of contact of tangents from a point on the circle to the circle touches the circle , then are in:AP EAMCET 2021 Medium
- The approximate value of \((1.0002)^{3000}\) isAP EAMCET 2002 Medium
- If the sum of the distances from a variable point to the given points and is , then the locus of isAP EAMCET 2019 Medium
More PYQs from AP EAMCET
- \(\lim _{n \rightarrow \infty}\left[\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+\ldots+\frac{1}{3 n}\right]=\)AP EAMCET 2017 Hard
- In quadrilateral is the midpoint of and is a point on such that . Then the points andAP EAMCET 2022 Medium
- The probability distribution of a discrete random variable X is given below
X = x -1 0 1 2 P(X = x) \(\frac{1}{3}\) \(\frac{1}{6}\) \(\frac{1}{6}\) \(\frac{1}{3}\)
Then the value of \(6 \Sigma\left(\mathrm{x}^2\right) \mathrm{P}(\mathrm{X}=\mathrm{x})-\operatorname{var}(\mathrm{X})=\)AP EAMCET 2025 Medium - If \(C\) is the mid-point of line segment \(A B\) and \(P\) is any point not on the line \(A B\), thenAP EAMCET 2021 Hard
- Two masses \(m_1\) and \(m_2\) are connected by a light string passing over smooth pulley. When set free \(m_1\) moves downwards by 3 m in 3 s . The ratio of \(\frac{m_1}{m_2}\) is \(\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)\)AP EAMCET 2024 Easy
- At \(T(\mathrm{~K})\), the vapour pressure of pure benzene is 0.85 bar. A non-volatile, non-electrolyte substance weighing \(0.5 \mathrm{~g}\) when added to \(39 \mathrm{~g}\) of benzene, the vapour pressure of the solution is 0.845 bar. The molar mass (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of the substance isAP EAMCET 2018 Medium