Question:
Equation of circle with centre \( (2,2) \) passing through \( (4,5) \)
Equation of circle with centre \( (2,2) \) passing through \( (4,5) \)
Show Hint
Use distance formula to find radius.
Updated On: May 1, 2026
- \( x^2+y^2-4x+4y-77=0 \)
- \( x^2+y^2-4x-4y-5=0 \)
- \( x^2+y^2+2x+2y-59=0 \)
- \( x^2+y^2-2x-2y-23=0 \)
- \( x^2+y^2+4x-2y-26=0 \)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept: Circle equation:
\[
(x-h)^2+(y-k)^2=r^2
\]
Step 1: Centre \( (2,2) \).
Step 2: Find radius.
\[ r^2=(4-2)^2+(5-2)^2=4+9=13 \]
Step 3: Write equation.
\[ (x-2)^2+(y-2)^2=13 \]
Step 4: Expand.
\[ x^2-4x+4 + y^2-4y+4=13 \]
Step 5: Simplify.
\[ x^2+y^2-4x-4y-5=0 \]
Step 1: Centre \( (2,2) \).
Step 2: Find radius.
\[ r^2=(4-2)^2+(5-2)^2=4+9=13 \]
Step 3: Write equation.
\[ (x-2)^2+(y-2)^2=13 \]
Step 4: Expand.
\[ x^2-4x+4 + y^2-4y+4=13 \]
Step 5: Simplify.
\[ x^2+y^2-4x-4y-5=0 \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM circle Questions
- If one end of a diameter of the circle \( x^2 + y^2 - 4x - 6y + 11 = 0 \) is \( (3, 4) \), then the coordinate of the other end of the diameter is:
- Find the area of the smaller segment cut-off from the circle \( x^2 + y^2 = 25 \) by \( x = 3 \):
- If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
- The radius of the circle \( x^2 + y^2 - 2x - 4y - 4 = 0 \) is:
- If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions