WBJEE · Maths · Circle
The equations of the circles, which touch both the axes and the line \(4 x+3 y=12\) and have centres in the first quadrant, are
- A \(x^{2}+y^{2}+x-y+1=0\)
- B \(x^{2}+y^{2}-2 x-2 y+1=0\)
- C \(x^{2}+y^{2}-12 x-12 y+36=0\)
- D \(x^{2}+y^{2}-6 x-6 y+36=0\)
Answer & Solution
Correct Answer
(C) \(x^{2}+y^{2}-12 x-12 y+36=0\)
Step-by-step Solution
Detailed explanation
Radius \((r)=\) perpendicular distance on line \(4 x+3 y=12\) from centre \(\Rightarrow \quad r=\frac{|4 r+3 r-12|}{\sqrt{16+9}}\) \(\Rightarrow \quad|7 r-12|=5 r\) \(\Rightarrow \quad 7 r-12=\pm 5 r\) \(\therefore \quad 2 r=12 \Rightarrow r=6\) and \(12 r=12 \Rightarrow r=1\)…
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 \(e^{\sin x}-e^{-\sin x}-4=0,\) then the number ofreal values of \(x\) isWBJEE 2019 Medium
- The value of the integral \(\int_{-2}^{2}(1+2 \sin x) e^{|x|} d x\) is
equal toWBJEE 2012 Easy - The straight line \(3 x+y=9\) divides the line segment joining the points \((1,3)\) and \((2,7)\) in the ratioWBJEE 2010 Medium
- \[
\text { If }(2 \leq r \leq n), \text { then }{ }^{n} C_{r}+2 \cdot{ }^{n} C_{r+1}+{ }^{n} C_{r+2} \text { is }
\]
equal toWBJEE 2018 Medium - \(F(x)=\cos x-1+\frac{x^2}{2!}, x \in \mathbb{R}\). Then \(f(x)\) isWBJEE 2024 Medium
- The population \(p(t)\) at time \(t\) of a certain mouse species follows the differential equation \(\frac{d p(t)}{d t}=0.5 p(t)-450\). If \(p(0)=850\), then the time at which the population becomes zero isWBJEE 2025 Medium
More PYQs from WBJEE
- The half-life of a radioactive element is 10 hours. How much will be left after 4 hours in \(1 \mathrm{~g}\) atom sample?WBJEE 2009 Hard
- From the focus of the parabola \(y^2=12 x\), a ray of light is directed in a direction making an angle \(\tan ^{-1} \frac{3}{4}\) with \(x\)-axis. Then the equation of the line along which the reflected ray leaves the parabola isWBJEE 2023 Medium
- The chord of the curve \(y=x^{2}+2 a x+b\) joining the points where \(x=\alpha\) and \(x=\beta,\) is parallel to the tangent to the curve at abscissa \(x\) is equal toWBJEE 2017 Medium
- A thin plastic sheet of refractive index 1.6 is used to cover one of the slits of a clouble slit arrangement. The central point on the scireen is now occupied by what would have been the 7th bright fringo before the plastic was used. If the wavelength of light is \(600 \mathrm{nm}\), what is the thickness (in \(\mu \mathrm{m}\) ) of the plastic sheet?WBJEE 2015 Medium
- In a region, the intensity of an electric field is given by \(\mathbf{E}=2 \mathbf{i}+3 \mathbf{j}+\mathbf{k}\) in \(\mathrm{NC}^{-1}\). The electric flux through a surface \(\mathbf{S}=10 \mathbf{i} \mathrm{m}^{2}\) in the region isWBJEE 2012 Easy
- What are the charges stored in the \(1 \mu \mathrm{~F}\) and \(2 \mu \mathrm{~F}\) capacitors in the circuit as shown in figure once the current (I) become steady?
WBJEE 2025 Medium