JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let \(C\) be the centre of the circle \(x^{2}+y^{2}-x+2 y=\) \(\frac{11}{4}\) and \(P\) be a point on the circle. A line passes through the point \(C\), makes an angle of \(\frac{\pi}{4}\) with the line \(C P\) and intersects the circle at the points \(Q\) and \(R\). Then the area of the triangle \(P Q R\) (in unit \({ }^{2}\) ) is.
- A \(2\)
- B \(2 \sqrt{2}\)
- C \(8 \sin \left(\frac{\pi}{8}\right)\)
- D \(8 \cos \left(\frac{\pi}{8}\right)\)
Answer & Solution
Correct Answer
(B) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(x ^{2}+ y ^{2}- x +2 y =\frac{11}{4}\) \(\left( x -\frac{1}{2}\right)^{2}+( y +1)^{2}=(2)^{2}\) Or \(\triangle PQR\) \(PR = QK \sin 2 \geq \frac{1}{3}\) \(=4 \cdot 6 \sin \frac{\pi}{8}\) \(PQ = QR \cos 22 \frac{1}{2}\) \(=4 \cos \frac{\pi}{8}\) As…
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 sum of the squares of the roots of \(|\mathrm{x}+2|^2+|\mathrm{x}-2|-2=0\) and the squares of the roots of \(x^2-2|x-3|-5=0\), isJEE Mains 2025 Medium
- Let \(f\left( x \right) = 5 - \left| {x - 2} \right|\) and \(g\left( x \right) = \left| {x + 1} \right|,x \in R\). If \(f(x)\) attains maximum value at \(\alpha \) and \(g(x)\) attains minimum value at \(\beta \), then \(\mathop {\lim }\limits_{x \to \alpha \beta } \frac{{\left( {x - 1} \right)\left( {{x^2} - 5x + 6} \right)}}{{{x^2} - 6x + 8}}\) is equal toJEE Mains 2019 Hard
- The number of elements in the set \(\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.\) and \(\left.(I-A)^{3}=I-A^{3}\right\}\) where \(I\) is \(2 \times 2\) identity matrix, is :JEE Mains 2021 Hard
- Let \(S=\{1,2,3, \ldots, 2022\}\). Then the probability, that a randomly chosen number \(n\) from the set \(S\) such that \(\operatorname{HCF}( n , 2022)=1\), is.JEE Mains 2022 Hard
- The integral \(\int{ \cfrac{d x}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}}\) is equal to (where \(\mathrm{C}\) is a constant of integration)JEE Mains 2020 Hard
- If \(a, b, c\) are sides of a scalene triangle, then the value of \(\left| \begin{array}{*{20}{c}}
a&b&c\\
b&c&a\\
c&a&b
\end{array} \right|\) isJEE Mains 2013 Hard
More PYQs from JEE Mains
- If \(C_{x} \equiv^{25} C_{x}\) and \(\mathrm{C}_{0}+5 \cdot \mathrm{C}_{1}+9 \cdot \mathrm{C}_{2}+\ldots .+(101) \cdot \mathrm{C}_{25}=2^{25} \cdot \mathrm{k}\) then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- Let \(\theta\) be the angle between the vectors \(\vec{a}\) and \(\vec{b}\), where \(|\vec{a}|=4,|\vec{b}|=3 \quad \theta \in\left(\frac{\pi}{4}, \frac{\pi}{3}\right)\). Then \(|(\vec{a}-\vec{b}) \times(\vec{a}+\vec{b})|^{2}+4(\vec{a} \cdot \vec{b})^{2}\) is equal toJEE Mains 2022 Medium
- Let \(R\) be a relation on \(N \times N\) defined by \((a, b) R\) (c, d) if and only if \(a d(b-c)=b c(a-d)\). Then \(R\) isJEE Mains 2023 Hard
- Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be a polynomial function of degree four having extreme values at \(x=4\) and \(x=5\).
If \(\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=5\), then \(f(2)\) is equal to :JEE Mains 2025 Medium - Let \( S=\{z\in\mathbb{C}:4z^{2}+\overline{z}=0\} \) Then \( \sum_{z\in S}|z|^{2} \) is equal to:JEE Mains 2026 Medium
- If the tangent at a point \(P,\) with parameter \(t,\) on the curve \(x = 4t^2 + 3,\,\,y = 8t^3 - 1,\,\,t \in R,\) meets the curve again at a point \(Q,\) then the coordinates of \(Q\) areJEE Mains 2016 Hard