Question:
The equation of a circle whose Centre is \((2,-1)\) and which passes through the point \((3,6)\) is
The equation of a circle whose Centre is \((2,-1)\) and which passes through the point \((3,6)\) is
Show Hint
If the circle passes through a point, use the distance formula from the centre to that point to find \(r^2\).
Updated On: May 7, 2026
- \(x^2+y^2+4x+2y-45=0\)
- \(x^2+y^2-2x+2y-50=0\)
- \(x^2+y^2+2x+2y-50=0\)
- \(x^2+y^2-4x+2y-45=0\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
The equation of a circle with centre \((h,k)\) is:
\[
(x-h)^2+(y-k)^2=r^2
\]
Step 1: Given centre is: \[ (2,-1) \] So the equation is: \[ (x-2)^2+(y+1)^2=r^2 \]
Step 2: The circle passes through \((3,6)\).
So radius is the distance between \((2,-1)\) and \((3,6)\). \[ r^2=(3-2)^2+(6+1)^2 \] \[ r^2=1^2+7^2 \] \[ r^2=1+49=50 \]
Step 3: Substitute \(r^2=50\). \[ (x-2)^2+(y+1)^2=50 \]
Step 4: Expand. \[ x^2-4x+4+y^2+2y+1=50 \] \[ x^2+y^2-4x+2y+5-50=0 \] \[ x^2+y^2-4x+2y-45=0 \] Therefore, \[ \boxed{x^2+y^2-4x+2y-45=0} \]
Step 1: Given centre is: \[ (2,-1) \] So the equation is: \[ (x-2)^2+(y+1)^2=r^2 \]
Step 2: The circle passes through \((3,6)\).
So radius is the distance between \((2,-1)\) and \((3,6)\). \[ r^2=(3-2)^2+(6+1)^2 \] \[ r^2=1^2+7^2 \] \[ r^2=1+49=50 \]
Step 3: Substitute \(r^2=50\). \[ (x-2)^2+(y+1)^2=50 \]
Step 4: Expand. \[ x^2-4x+4+y^2+2y+1=50 \] \[ x^2+y^2-4x+2y+5-50=0 \] \[ x^2+y^2-4x+2y-45=0 \] Therefore, \[ \boxed{x^2+y^2-4x+2y-45=0} \]
Was this answer helpful?
0
0
Top AP ECET Mathematics Questions
- The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is
- A random variable X has the following probability distribution The variance of this random variable is
- For the matrix $A = \begin{pmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{pmatrix}, A^{-1} = $
- If $A = \begin{bmatrix}k/2&0&0\\ 0&1/3&0\\ 0&0&m/4\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}1/2&0&0\\ 0&1/3&0\\ 0&0&1/4\end{bmatrix}$ then $ k + l + m = $
- Number of ways of forming a committee of $6$ members out of $5$ Indians, $5$ Americans and $5$ Australians such that there will be atleast one member from each country in the committee is
View More Questions
Top AP ECET circle Questions
- In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
- The length of the tangent from the point \((5,1)\) to the circle \(x^2+y^2+6x-4y-3=0\) is
- If length of the tangent is \(8\text{ cm}\) and the distance between the center of the circle and the external point is \(11\text{ cm}\), then the area of the circle is
- The equation of a circle whose Centre is \((-3,2)\) and area is \(176\) units is
- In a circle with center \(O\), a \(6\text{ cm}\) long chord is at a distance \(4\text{ cm}\) from the center. Then the length of diameter is
View More Questions
Top AP ECET Questions
- The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is
- Thermal decomposition of $HCOOH$ is a first order reaction and the rate constant at T(K) is $4.606 \times 10^{-3}\, s^{-1}$. The time required to decompose $90\%$ of initial quantity of $HCOOH$ at $T(K)$ in seconds is
- Three rods of same dimensions have thermal conductivities 3 K, 2 K and K. They are arranged as shown below:What will be the temperature T of the junction?
- To which group and period does the element belong if the electronic configuration of an element in its $-2$ oxidation state is $1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}$ ?
- A ball of mass 0.6 kg attached to a light inextensible string rotates in a vertical circle of radius 0.75 m such that it has a speed of $ 5\text{ }m{{s}^{-1}} $ when the string is horizontal. Tension in string when it h horizontal on other side is $ (g=10m{{s}^{-}}2) $
View More Questions