MHT CET · Maths · Circle
Two circles centered at \((2,3)\) and \((4,5)\) intersects each other. If their radii are equal, then the equation of the common chord is
- A \(x+y+1=0\)
- B \(x+y-1=0\)
- C \(x+y-7=0\)
- D \(x+y+7=0\)
Answer & Solution
Correct Answer
(C) \(x+y-7=0\)
Step-by-step Solution
Detailed explanation
Equation of common chord is \(S_1-S_2=0\), where \(S_1\) and \(S_2\) are equations of the circles
\(\therefore\left[(\mathrm{x}-2)^2+(\mathrm{y}-3)^2\right]-\left[(\mathrm{x}-4)^2+(\mathrm{y}-5)^2\right]\) \(=0 \)
\( \therefore-4 \mathrm{x}+4-6 \mathrm{y}+9+8 \mathrm{x}-16+10 \mathrm{y}-25=0 \)
\( \therefore 4 \mathrm{x}+4 \mathrm{y}-28=0 \quad \Rightarrow \mathrm{x}+\mathrm{y}=7 \)
\(\therefore\left[(\mathrm{x}-2)^2+(\mathrm{y}-3)^2\right]-\left[(\mathrm{x}-4)^2+(\mathrm{y}-5)^2\right]\) \(=0 \)
\( \therefore-4 \mathrm{x}+4-6 \mathrm{y}+9+8 \mathrm{x}-16+10 \mathrm{y}-25=0 \)
\( \therefore 4 \mathrm{x}+4 \mathrm{y}-28=0 \quad \Rightarrow \mathrm{x}+\mathrm{y}=7 \)
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 \(\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}\), then the value of \(x\) isMHT CET 2024 Medium
- The slopes of the lines represented by \(6 x^2+2 \mathrm{~h} x \mathrm{y}+\mathrm{y}^2=0\) are in the ratio \(2: 3\), then \(\mathrm{h}=\)MHT CET 2025 Medium
- \(\int_{-1}^1 \log \left(\frac{2-x}{2+x}\right) d x=\)MHT CET 2022 Medium
- The distance of a point \((1,2,-1)\) from the plane \(x-2 y+4 z+10=0\) isMHT CET 2020 Easy
- If \(x=1+2 i\), then the value of \(x^3+7 x^2-x+16\) isMHT CET 2021 Medium
- If the lines \(\frac{x-1}{2}=\frac{\mathrm{y}+1}{3}=\frac{\mathrm{z}-1}{4}\) and \(\frac{x-3}{1}=\frac{\mathrm{y}-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}\) interect, then the value of the \(\mathrm{k}\) isMHT CET 2020 Easy
More PYQs from MHT CET
- The Henry's law constant for oxygen is \(1 \cdot 3 \times 10^{-3} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~atm}^{-1}\). If partial pressure of oxygen is \(0.46\) atmosphere what is the concentration of dissolved oxygen at \(25^{\circ} \mathrm{C}\) and 1 atm pressure?MHT CET 2020 Easy
- If is a function defined by then range isMHT CET 2018 Hard
- Identify the element if it's observed and expected electronicMHT CET 2022 Easy
- An n-p-n transistor can be considered to be equivalent to two diodes connected. The correct figure out of the following is
(a)
(b)
(c)
(d)
MHT CET 2024 Easy - If two planets have their radii in the ratio \(x: y\) and densities in the ratio \(m: n\), then the acceleration due to gravity on them are in the ratioMHT CET 2023 Medium
- A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ( \(g=\) acceleration due to gravity)
MHT CET 2025 Medium