Question:
The radical centre of the system of circles,
\[
x^2 + y^2 + 4x + 7 = 0,\quad
2(x^2 + y^2) + 3x + 5y + 9 = 0
\]
and \(x^2 + y^2 + y = 0\) is
The radical centre of the system of circles,
\[
x^2 + y^2 + 4x + 7 = 0,\quad
2(x^2 + y^2) + 3x + 5y + 9 = 0
\]
and \(x^2 + y^2 + y = 0\) is
Show Hint
Radical center = solve pairwise subtractions of circle equations.
Updated On: Apr 16, 2026
- \((-2,-1)\)
- \((1,-2)\)
- \((-1,-2)\)
- None of these
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
Radical center = intersection of radical axes.
Step 1: Subtract equations.
Between first and second: \[ x^2+y^2+4x+7 - [2(x^2+y^2)+3x+5y+9]=0 \] \[ \Rightarrow -x^2 -y^2 + x -5y -2=0 \]
Step 2: Subtract first and third.
\[ (x^2+y^2+4x+7)-(x^2+y^2+y)=0 \Rightarrow 4x - y + 7=0 \]
Step 3: Solve.
Solving gives: \[ (-2,-1) \]
Step 1: Subtract equations.
Between first and second: \[ x^2+y^2+4x+7 - [2(x^2+y^2)+3x+5y+9]=0 \] \[ \Rightarrow -x^2 -y^2 + x -5y -2=0 \]
Step 2: Subtract first and third.
\[ (x^2+y^2+4x+7)-(x^2+y^2+y)=0 \Rightarrow 4x - y + 7=0 \]
Step 3: Solve.
Solving gives: \[ (-2,-1) \]
Was this answer helpful?
0
0
Top MET Mathematics Questions
- Let \( f:\mathbb{N} \to \mathbb{N} \) be defined as \[ f(n)= \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] Then \( f \) is:
- MET - 2024
- Mathematics
- types of functions
- Given vectors \(\vec{a}, \vec{b}, \vec{c}\) are non-collinear and \((\vec{a}+\vec{b})\) is collinear with \((\vec{b}+\vec{c})\) which is collinear with \(\vec{a}\), and \(|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}\), find \(|\vec{a}+\vec{b}+\vec{c}|\).
- MET - 2024
- Mathematics
- Addition of Vectors
- Given \(\frac{dy}{dx} + 2y\tan x = \sin x\), \(y=0\) at \(x=\frac{\pi}{3}\). If maximum value of \(y\) is \(1/k\), find \(k\).
- MET - 2024
- Mathematics
- Differential equations
- If \(x = \sin(2\tan^{-1}2)\), \(y = \sin\left(\frac{1}{2}\tan^{-1}\frac{4}{3}\right)\), then:
- MET - 2024
- Mathematics
- Properties of Inverse Trigonometric Functions
- Let \( D = \begin{vmatrix} n & n^2 & n^3 \\ n^2 & n^3 & n^5 \\ 1 & 2 & 3 \end{vmatrix} \). Then \( \lim_{n \to \infty} \frac{M_{11} + C_{33}}{(M_{13})^2} \) is:
- MET - 2024
- Mathematics
- Determinants
View More Questions
Top MET circle Questions
- The equation of mirror image of the circle \(x^2 + y^2 - 6x - 10y + 33 = 0\) about the line \(y = x\) is:
- If the angle between the pair of straight lines formed by joining the points of intersection of \(x^2 + y^2 = 4\) and \(y = 3x + c\) to the origin is a right angle, then \(c^2\) is:
- The number of common tangents to two circles \(x^2 + y^2 = 4\) and \(x^2 + y^2 - 8x + 12 = 0\) is:
- The point on the straight line \(y = 2x + 11\) which is nearest to the circle \(16(x^2 + y^2) + 32x - 8y - 50 = 0\), is
- The locus of centre of circles which cut orthogonally the circle \(x^2 + y^2 - 4x + 8 = 0\) and touches \(x + 1 = 0\), is
View More Questions
Top MET Questions
- Let \( f:\mathbb{N} \to \mathbb{N} \) be defined as \[ f(n)= \begin{cases} \frac{n+1}{2}, & \text{if } n \text{ is odd} \\ \frac{n}{2}, & \text{if } n \text{ is even} \end{cases} \] Then \( f \) is:
- MET - 2024
- types of functions
- Given vectors \(\vec{a}, \vec{b}, \vec{c}\) are non-collinear and \((\vec{a}+\vec{b})\) is collinear with \((\vec{b}+\vec{c})\) which is collinear with \(\vec{a}\), and \(|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}\), find \(|\vec{a}+\vec{b}+\vec{c}|\).
- MET - 2024
- Addition of Vectors
- Given \(\frac{dy}{dx} + 2y\tan x = \sin x\), \(y=0\) at \(x=\frac{\pi}{3}\). If maximum value of \(y\) is \(1/k\), find \(k\).
- MET - 2024
- Differential equations
- Let \( f(x) \) be a polynomial such that \( f(x) + f(1/x) = f(x)f(1/x) \), \( x > 0 \). If \( \int f(x)\,dx = g(x) + c \) and \( g(1) = \frac{4}{3} \), \( f(3) = 10 \), then \( g(3) \) is:
- MET - 2024
- Definite Integral
- A real differentiable function \(f\) satisfies \(f(x)+f(y)+2xy=f(x+y)\). Given \(f''(0)=0\), then \[ \int_0^{\pi/2} f(\sin x)\,dx = \]
- MET - 2024
- Definite Integral
View More Questions