JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
A circle with centre \((2,3)\) and radius \(4\) intersects the line \(x + y =3\) at the points \(P\) and \(Q\). If the tangents at \(P\) and \(Q\) intersect at the point \(S(\alpha, \beta)\), then \(4 \alpha-7 \beta\) is equal to \(........\).
- A \(11\)
- B \(10\)
- C \(80\)
- D \(90\)
Answer & Solution
Correct Answer
(A) \(11\)
Step-by-step Solution
Detailed explanation
The given line is polar or \(P (2, \beta)\) w.r.t. given circle \(x^2+y^2-4 x-6 y-3=0\) Chord or contact \(\alpha x+\beta y-2(x+\alpha)-3(y+\beta)-3=0\) \(\Rightarrow(\alpha-2) x+(\beta-3) y-(2 \alpha+3 \beta+3)=0\) \(\because\) But the equation of chord of contact is given 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
- Let \(x, y>0\). If \(x^{3} y^{2}=2^{15}\), then the least value of \(3 x +2 y\) isJEE Mains 2022 Hard
- Let \(R\,= \{(x,y) : x,y \in N\, and\, x^2 -4xy +3y^2\, =0\}\), where \(N\) is the set of all natural numbers. Then the relation \(R\) isJEE Mains 2013 Hard
- let \(y = y\left( x \right)\) be the solution of the differential equation \(\sin x\frac{{dy}}{{dx}} + ycos\;x = 4x\;\), \(x \in \left( {0,\pi } \right)\) . If \(y\left( {\frac{\pi }{2}} \right) = 0\) then \(y\left( {\frac{\pi }{6}} \right) = .\;.\;..\;\) .JEE Mains 2018 Hard
- If a curve \(y=y(x)\) passes through the point \(\left(1, \frac{\pi}{2}\right)\) and satisfies the differential equation \(\left(7 x^4 \cot y-e^x \operatorname{cosec} y\right) \frac{d x}{d y}=x^5, x \geq 1\), then at \(x=2\), the value of cosy is:JEE Mains 2025 Medium
- Let \(x\) and \(y\) be distinct integers where \(1 \leq x \leq 25\) and \(1 \leq y \leq 25\). Then, the number of ways of choosing \(x\) and \(y\), such that \(x + y\) is divisible by \(5\) , is \(.........\).JEE Mains 2023 Hard
- Let \(\mathrm{P}\) be a plane passing through the points \((2,1,0),(4,1,1)\) and \((5,0,1)\) and \(R\) be any point \((2,1,6) .\) Then the image of \(\mathrm{R}\) in the plane \(\mathrm{P}\) isJEE Mains 2020 Hard
More PYQs from JEE Mains
- For the system of linear equations \(2 x-y+3 z=5\) \(3 x+2 y-z=7\) \(4 x+5 y+\alpha z=\beta\) Which of the following is NOT correct ?JEE Mains 2023 Hard
- If \(y = {\rm{sec}}\left( {{{\tan }^{ - 1}}x} \right)\) then \(\frac{{dy}}{{dx}}\) at \(x = 1\) is equal to :JEE Mains 2013 Medium
- Let C be the circle \(\mathrm{x}^2+(\mathrm{y}-1)^2=2, \mathrm{E}_1\) and \(\mathrm{E}_2\) be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line \(x+y=3\) touch the curves \(C\), \(E_1\) and \(E_2\) at \(P\left(x_1, y_1\right), Q\left(x_2, y_2\right)\) and \(R\left(x_3, y_3\right)\) respectively. Given that \(P\) is the mid-point of the line segment \(Q R\) and \(P Q=\frac{2 \sqrt{2}}{3}\), the value of \(9\left(x_1 y_1+x_2 y_2+x_3 y_3\right)\) is equal to ______ .JEE Mains 2025 Hard
- The number of real solution(s) of the equation \(x^2+3 x+2=\min \{|x-3|,|x+2|\} \text { is : }\)JEE Mains 2025 Medium
- The number of solutions of equation \((4-\sqrt{3}) \sin x\) \(-2 \sqrt{3} \cos ^2 x=-\frac{4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}\right]\) isJEE Mains 2025 Medium
- If \(\lim _{x \rightarrow \infty}\left(\sqrt{x^{2}-x+1}-a x\right)=b\), then the ordered pair \((a, b)\) is:JEE Mains 2021 Hard