
How do you find the center and radius of the circle ?
Answer
479.1k+ views
Hint: This type of question is based on the concept of the equation of a circle. Here, to explain the concept let us consider the standard equation of a circle, that is, . Here, (h,k) is the centre of the circle and ‘r’ is the radius. By comparing the standard equation of circle and the given circle, we get h=3 and k=0. Thus, we get the centre of the given circle. Similarly, comparing the standard equation of circle with the given circle, we get . Taking the square root on both the sides, we get the radius of the circle.
Complete answer:
According to the question, we are asked to find the radius and center of the circle .
We have been given the equation of the circle is . --------(1)
Let us first consider the standard equation of a circle.
---------(2)
Here, h is a point in the x-axis and k is a point in the y-axis.
Therefore, the centre of this circle is (h,k).
Also the radius of the circle is ‘r’.
On comparing equation (1) with equation (2), we get
h=3 and k=0.
Therefore, the centre of the circle is (3,0).
Also by comparing the standard equation of circle with the given circle,
We get . --------(3)
Let us take square root on both sides of the equation (3).
But we know that .
Also we know that .
Using this in the above obtained expression, we get
Therefore, the radius of the circle is 2 units.
Hence, the centre and radius of the circle is (3,0) and 2 respectively.
Note: We can also solve this type of question by plotting the graph.
The given equation is .
On taking square root on both the sides, we get,
On substituting any value of x from x- axis, we get a corresponding term y from y-axis.
On plotting a graph with the obtained points, we get
Therefore, from the circle obtained from plotting the graph, we find that the centre is (3,0) and radius is 2 units.
Complete answer:
According to the question, we are asked to find the radius and center of the circle
We have been given the equation of the circle is
Let us first consider the standard equation of a circle.
Here, h is a point in the x-axis and k is a point in the y-axis.
Therefore, the centre of this circle is (h,k).
Also the radius of the circle is ‘r’.
On comparing equation (1) with equation (2), we get
h=3 and k=0.
Therefore, the centre of the circle is (3,0).
Also by comparing the standard equation of circle with the given circle,
We get
Let us take square root on both sides of the equation (3).
But we know that
Also we know that
Using this in the above obtained expression, we get
Therefore, the radius of the circle is 2 units.
Hence, the centre and radius of the circle
Note: We can also solve this type of question by plotting the graph.
The given equation is
On taking square root on both the sides, we get,
On substituting any value of x from x- axis, we get a corresponding term y from y-axis.
On plotting a graph with the obtained points, we get

Therefore, from the circle obtained from plotting the graph, we find that the centre is (3,0) and radius is 2 units.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Biology: Engaging Questions & Answers for Success

Class 12 Question and Answer - Your Ultimate Solutions Guide

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Social Science: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Father of Indian ecology is a Prof R Misra b GS Puri class 12 biology CBSE

Who is considered as the Father of Ecology in India class 12 biology CBSE

Enzymes with heme as prosthetic group are a Catalase class 12 biology CBSE

An example of ex situ conservation is a Sacred grove class 12 biology CBSE

An orchid growing as an epiphyte on a mango tree is class 12 biology CBSE

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE
