JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let the lines \((2-i) z=(2+i) \bar{z}\) and \((2+i) z+(i-2) \bar{z}-4 i=0,\) (here \(\left.i^{2}=-1\right)\) be normal to a circle \(C\). If the line \(iz +\overline{ z }+1+ i =0\) is tangent to this circle \(C\), then its radius is
- A \(\frac{3}{\sqrt{2}}\)
- B \(\frac{1}{2 \sqrt{2}}\)
- C \(3 \sqrt{2}\)
- D \(\frac{3}{2 \sqrt{2}}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\((i)\) \((2- i ) z =(2+ i ) \overline{ z }\) \(y=\frac{x}{2}\) \((ii)\) \((2+ i ) z +( i -2) \overline{ z }-4 i =0\) \(x+2 y=2\) \((iii)\) \(iz +\overline{ z }+1+ i =0\) \(Eq ^{ n }\) of tangent \(x - y +1=0\) Solving \((i)\) and \((ii)\) \(x=1, y=\frac{1}{2}\) Now,…
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
- Let \(A=\left(\begin{array}{rrr}1 & -1 & 0 \\ 0 & 1 & -1 \\ 0 & 0 & 1\end{array}\right)\) and \(B=7 A^{20}-20 A^{7}+2 I\), where \(I\) is an identity matrix of order \(3 \times 3\) If \(B=\left[b_{i j}\right]\), then \(b_{13}\) is equal to \(....\)JEE Mains 2021 Hard
- If the area of the region bounded by the curves \(y^2-2 y=-x, x+y=0\) is \(A\), then \(8 A\) is equal toJEE Mains 2023 Hard
- If \(m\) is a non-zero number and \(\int \frac{x^{5 m-1}+2 x^{4 m-1}}{\left(x^{2 m}+x^{m}+1\right)^{3}} d x=f(x)+c\) , then \(f(x)\) isJEE Mains 2014 Hard
- Let \(a\), \(b\) be two non-zero real numbers. If \(p\) and \(r\) are the roots of the equation \(x ^{2}-8 ax +2 a =0\) and \(q\) and \(s\) are the roots of the equation \(x^{2}+12 b x+6 b\) \(=0\), such that \(\frac{1}{ p }, \frac{1}{ q }, \frac{1}{ r }, \frac{1}{ s }\) are in A.P., then \(a ^{-1}- b ^{-1}\) is equal to \(......\)JEE Mains 2022 Hard
- Let the mirror image of a circle \(c_{1}: x^{2}+y^{2}-2 x-\) \(6 y+\alpha=0\) in line \(y=x+1\) be \(c_{2}: 5 x^{2}+5 y^{2}+10 g x\) \(+10 f y +38=0\). If \(r\) is the radius of circle \(c _{2}\), then \(\alpha+6 r^{2}\) is equal to\(.....\)JEE Mains 2022 Hard
- Let \(S\) be the set of all values of \(\lambda\), for which the shortest distance between the lines \(\frac{x-\lambda}{0}=\frac{y-3}{4}=\frac{z+6}{1}\) and \(\frac{x+\lambda}{3}=\frac{y}{-4}=\frac{z-6}{0}\) is \(13\) Then \(8\left|\sum_{\lambda \in S} \lambda\right|\) is equal toJEE Mains 2023 Medium
More PYQs from JEE Mains
- If \(A\) and \(B\) are two non-zero \(n \times n\) matrics such that \(A ^2+ B = A ^2 B\), thenJEE Mains 2023 Hard
- Box \(I\) contains \(30\) cards numbered \(1\) to \(30\) and Box \(II\) contains \(20\) cards numbered \(31\) to \(50 .\) A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box \(I\) isJEE Mains 2020 Hard
- If \(\lim _{x \rightarrow 0} \frac{\alpha e^{x}+\beta e^{-x}+\gamma \sin x}{x \sin ^{2} x}=\frac{2}{3}\), where \(\alpha, \beta, \gamma \in R\), then which of the following is \(NOT\) correct ?JEE Mains 2022 Hard
- Let \(f: R \rightarrow R\) be defined as \(f(\mathrm{x})= -\frac{4}{3} x^{3}+2 x^{2}+3 x ,\quad x>0\) \(\quad\quad\quad\quad 3 x e^{x}, \quad\quad\quad\quad\quad\quad\mathrm{x} \leq 0\) Then \(\mathrm{f}\) is increasing function in the interval.JEE Mains 2021 Medium
- Five numbers \(x _{1}, x _{2}, x _{3}, x _{4}, x _{5}\) are randomly selected from the numbers \(1,2,3, \ldots \ldots, 18\) and are arranged in the increasing order \(\left( x _{1}< x _{2}< x _{3}< x _{4}< x _{5}\right)\). The probability that \(x_{2}=7\) and \(x_{4}=11\) isJEE Mains 2022 Hard
- \(\max _{0 \leq x \leq \pi}\left\{x-2 \sin x \cos x+\frac{1}{3} \sin 3 x\right\}=\)JEE Mains 2023 Hard