WBJEE · Maths · Circle
Let \(P\) be a variable point on a circle \(C\) and \(Q\) be a fixed point outside \(C\). If \(R\) is the midpoint of the line segment \(P Q\), then locus of \(R\) is
- A a circle
- B a circle and a pair of straight lines
- C a rectangular hyperbola
- D a pair of sraight lines
Answer & Solution
Correct Answer
(A) a circle
Step-by-step Solution
Detailed explanation
Let circle be \(\left(x-x_{1}\right)=r \cos \theta\) \(y-y_{1}=r \sin \theta\) \(h=\frac{a+x_{1}+r \cos \theta}{2}\) \(k=\frac{b+y_{1}+r \sin \theta}{2}\)…
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 \(i=\sqrt{-1}\) and \(n\) is a positive integer, then \(i^n+i^{n+1}+i^{n+2}+i^{n+3}\) is euqal toWBJEE 2009 Easy
- The numbers \(1,2,3, \ldots . . \mathrm{n}\) are arrange in a random order. The probability that the digits \(1,2,3, \ldots ., k(kWBJEE 2024 MediumLet \(y=f(x)\) be any curve on the \(X-Y\) plane \& \(P\) be a point on the curve. Let \(C\) be a fixed point not on the curve. The length \(P C\) is either a maximum or a minimum, thenWBJEE 2024 MediumThe value of \(\lim _{x \rightarrow 0^{+}} \frac{x}{p}\left[\frac{q}{x}\right]\) isWBJEE 2019 EasyIf the sum of the squares of the roots of the equation \(x^2-(a-2) x-(a+1)=0\) is least for an appropriate value of the variable parameter \(a\), then the value of ' \(a\) ' will beWBJEE 2025 Medium
From WBJEE More PYQs from WBJEE
- If for a matrix \(A,|A|=6\) and adj \(A=\left[\begin{array}{ccc}1 & -2, & 4 \\ 4 & 1 & 1 \\ -1 & k & 0\end{array}\right]\), then \(k\) is equal toWBJEE 2025 Medium
- Two pith balls, each carrying charge \(+q\) are hung from a hook by two strings. It is found that when each charge is tripled, angle between the strings double. What was the initial angle between the strings?WBJEE 2020 Hard
- In which of the following pairs, the two physical quantities have different dimensions?WBJEE 2014 Easy
- A point object is placed on the axis of a thin convex lens of focal length \(0.05 \mathrm{m}\) at a distance of \(0.2 \mathrm{m}\) from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of \(A \mathrm{cm},\) then what is the amplitude of oscillation of the image? \(\left[\right.\) you may assume, \(\frac{1}{1+x} \approx 1-x,\) where \(\left.x< < 1\right]\)WBJEE 2019 Hard
- Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be vectors of equal magnitude such that the angle between \(\vec{a}\) and \(\vec{b}\) is \(\alpha, \vec{b}\) and \(\vec{c}\) is \(\beta\) and \(\vec{c}\) and \(\vec{a}\) is \(\gamma\). Then the minimum value of \(\cos \alpha+\cos \beta+\cos \gamma\) isWBJEE 2025 Medium
- The de-Broglie wavelength of a moving bus with speed is \(v\) is \(\lambda\). Some passengers left the bus at a stoppage. Now when the bus moves with twice of its initial speed. Its kinetic energy is found to be twice of its value. What is the de-Broglie wavelength of the bus now?WBJEE 2025 Medium