AP EAMCET · Maths · Circle
If \(x+y-1=0\) and \(2 x-y+1=0\) are conjugate lines with respect to a circle \(x^2+y^2-4 x+2 f y-1=0\), then \(f=\)
- A -1 or 3
- B 1 or 2
- C -2 or 0
- D -1 or 2
Answer & Solution
Correct Answer
(C) -2 or 0
Step-by-step Solution
Detailed explanation
Conjugate lines are : \(x+y-1=0,2 x-y+1=0\) \(\mathrm{l}_1=1, \mathrm{~m}_1=1, \mathrm{n}_1=-1, \mathrm{l}_2=2, \mathrm{~m}_2=-1, \mathrm{n}_2=1\) \(\begin{aligned} & \therefore \quad g=-2, c=-1 \\ & \text { Radius, } R=\sqrt{f^2+4+1}=\sqrt{f^2+5}\end{aligned}\) Now, the…
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
- If \(\sin ^4 \theta \cos ^2 \theta=\sum_{n=0}^{\infty} a_{2 n} \cos 2 n \theta\), then the least \(n\) for which \(a_{2 n}=0\) isAP EAMCET 2022 Medium
- The equation of a circle which touches the straight lines \(x+y=2, x-y=2\) and also touches the circle \(x^2+y^2=1\), isAP EAMCET 2017 Medium
- Let the points \(\mathrm{P}_1\left(\frac{\pi}{4}\right), \mathrm{P}_2\left(\frac{3 \pi}{4}\right), \mathrm{P}_3\left(\frac{5 \pi}{4}\right)\) and \(\mathrm{P}_4\left(\frac{7 \pi}{4}\right)\) given in parametric form, lie on the hyperbola \(\frac{x^2}{9}-\frac{y^2}{16}=1\). Then these four points in that order formAP EAMCET 2023 Easy
- If \(A(1,2,0), B(2,0,1), C(-3,0,2)\) are the vertices of \(\triangle A B C\), then the length of the internal bisector of \(\angle \mathrm{BAC}\) isAP EAMCET 2024 Easy
- A candidate takes three tests in succession and the probability of passing the first test is \(p\). The probability of passing each succeeding test is \(p\) or \(\frac{p}{2}\) according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, isAP EAMCET 2014 Easy
- A college student has to appear for two examinations A and B. The probabilities that the student passes in A and B are \(\frac{2}{3}\) and \(\frac{3}{4}\) respectively. If it is known that the student passes at least one among the two examinations, then the probability that the student will pass both the examinations isAP EAMCET 2017 Hard
More PYQs from AP EAMCET
- The area (in square units) of the triangle formed by the X - axis, the tangent and the normal drawn at \((1,1)\) to the curve \(x^3+y^3=2 x y\) isAP EAMCET 2025 Medium
- At \(27^{\circ} \mathrm{C}\). the degree of dissociation of HA (weak acid) in 0.5 M of its solution is \(1 \%\). The concentrations of \(\mathrm{H}_3 \mathrm{O}^{-}\), \(\mathrm{A}^{-}\)and HA at equilibrium (in \(\mathrm{mol} \mathrm{L}^{-1}\) ) are respectivelyAP EAMCET 2024 Medium
- Which one of the following statements is correct?AP EAMCET 2013 Medium
- When the coordinate axes are rotated through an angle of \(45^{\circ}\) about the origin in the positive direction, if the transformed equation of a curve is \(17 x^2-16 x y+17 y^2=225\), then the original equation of that curve isAP EAMCET 2018 Medium
- The coordinates of the point which divides the line joining the points \((2,3,4)\) and \((3,-4,7)\) in the ratio \(2: 4\) externally isAP EAMCET 2023 Easy
- What is the molar mass (in \(\mathrm{g} \mathrm{mol}^{-1}\) ) of a substance, which forms a \(7 \%\) by mass solution in water, which freezes at \(-0.93^{\circ} \mathrm{C}\) ? \(\left(\mathrm{K}_{\mathrm{f}}\right.\) of \(\left.\mathrm{H}_2 \mathrm{O}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)AP EAMCET 2017 Medium