AP EAMCET · Maths · Straight Lines
The line on which the lines \(a x+b y=1\) and \(b x+a y=1\) (with \(a \neq 0 \neq b\) ) intersect for any real values of \(a\) and \(b\) is
- A \(x=-y\)
- B \(x=2 y\)
- C \(2 x=y\)
- D \(x=y\)
Answer & Solution
Correct Answer
(D) \(x=y\)
Step-by-step Solution
Detailed explanation
Lines : \(a x+b y=1\)...(i) \(b x+a y=1\)...(ii) [Multiply Eq. (i) by \(b\) ] - [Multiply Eq. (ii) by \(a\) ] \(a b x+b^2 y-a b x-a^2 y=b-a\) \(\Rightarrow \quad y=\frac{b-a}{b^2-a^2}=\frac{1}{a+b}\) Put \(y=\frac{1}{a+b}\) in Eq. (i), \(a x=1-\frac{b}{a+b}=\frac{a}{a+b}\)…
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 scalar product of the vector with a unit vector along the sum of the vectors and is equal to one. Then.AP EAMCET 2020 Medium
- The angle between the tangents drawn from the origin to the circle \(x^2+y^2+4 x-6 y+4=0\) isAP EAMCET 2016 Medium
- \(\mathrm{A}(4,3), \mathrm{B}(2,5)\) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoint of \(A B\), then the locus of \(P\) isAP EAMCET 2025 Medium
- Match the points on the curve \(2 y^2=x+1\) with the slopes of normals at those points and choose the correct answer.
AP EAMCET 2004 Hard - \(\lim _{x \rightarrow \frac{\pi}{2}} \frac{1+\cos 2 x}{\cot 3 x\left(3^{\sin 2 x}-1\right)}=\)AP EAMCET 2018 Medium
- \(A(a, 0)\) is a fixed point and \(\theta\) is a parameter such that \(0 < \theta < 2 \pi\). If \(\mathrm{P}(\mathrm{a} \cos \theta, \mathrm{a} \sin \theta)\) is a point on the circle \(\mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2\) and \(\mathrm{Q}(\mathrm{b} \sin \theta,-\mathrm{b} \cos \theta)\) is a point on the circle \(x^2+y^2=b^2\), then the locus of the centroid of the triangle APQ isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- If \(1, \omega, \omega^2\) denote the cube roots of unity, then the value of \(\left(1-\omega+\omega^2\right)^5+\left(1+\omega-\omega^2\right)^5\) isAP EAMCET 2022 Easy
- If \(\bar{u}, \bar{v}, \bar{w}\) are non coplanar vectors and \(p, q\) are real numbers, then the equality \(\left[\begin{array}{lll}3 \overline{\mathrm{u}} & \mathrm{p} \overline{\mathrm{v}} & \mathrm{p} \overline{\mathrm{w}}\end{array}\right]-\left[\begin{array}{lll}\mathrm{p} \overline{\mathrm{v}} & \overline{\mathrm{w}} & \mathrm{q} \overline{\mathrm{u}}\end{array}\right]-\left[\begin{array}{lll}2 \overline{\mathrm{w}} & \mathrm{q} \overline{\mathrm{v}} & \mathrm{q} \overline{\mathrm{u}}\end{array}\right]=0\) holds forAP EAMCET 2025 Medium
- Which of the following statement is not correct for glucose ?AP EAMCET 2025 Medium
- If \(A=\left[\begin{array}{ccc}1 & 2 & -2 \\ 2 & -1 & 2 \\ -1 & 1 & -2\end{array}\right]\), then \(A+2 A^{-1}=\)AP EAMCET 2025 Medium
- The number of \(d\) electrons in Fe is equal to which of the following?
i. Total number of ' \(s\) ' electrons of Mg
ii. Total number of ' \(p\) ' electrons of Cl
iii. Total number of ' \(p\) ' electrons of Ne
The correct option isAP EAMCET 2024 Easy - The standard reduction potentials of \(2 \mathrm{H}^{+} / \mathrm{H}_2, \mathrm{Cu}^{2+} / \mathrm{Cu}\). \(\mathrm{Zn}^{2+} / \mathrm{Zn}\) and \(\mathrm{NO}_3{ }^{-}, \mathrm{H}^{+} / \mathrm{NO}\) are \(0.0,-0.34,-0.76\) and 0.97 V respectively. Observe the following reactions
I. \(\mathrm{Zn}+\mathrm{HCl} \rightarrow\)
II. \(\mathrm{Cu}+\mathrm{HCl} \rightarrow\)
III. \(\mathrm{Cu}+\mathrm{HNO}_3 \rightarrow\)
Which reactions does not liberate \(\mathrm{H}_2(\mathrm{~g})\) ?AP EAMCET 2024 Medium