Circle: Particular Cases of a Circle and Solved Examples

On the rectangular coordinate system, there are infinite points where the center of a circle can lie, and accordingly the equation of the circle changes. Let’s discuss some special cases to write the equation of a circle under such conditions with the help of some examples.

Table of Contents

Particular cases of a Circle
Practice Problems
FAQs

Particular Cases of a Circle

Practice Problems of Particular cases of a Circle

Q1. Find the equation(s) of the circle which touches the at the point and cuts an intercept of length on the .

Answer. According to the given information in the question we can conclude that there can be two circles touching the at and cutting the The center of the one circle lies in the first quadrant and other in the second quadrant as shown in the figure below.

Radius

Centre

Hence, the required equation of the circle(s) is or

Q2. Find the equation of a circle touching both the coordinate axes and the straight line in the quadrant and lies below it.

Answer.

Since the circle touches both the axes in the first quadrant, the coordinates of the center of circle can be where is the radius of the circle.

Distance between the center and the line is the radius of the circle.

But, since on putting and in gives the same sign, it implies that they lie on the same side of the given line, whereas and lie on the opposite sides.

Center of the given circle is and radius is

Hence, the required equation of the circle is or

Q3. Find the equation of a circle whose center lies on the -axis which passes through and the radius is units.

Answer. Given, the centre lies on the -axis. Let the coordinates of the centre be .

Radius units

Case 1 :

∴ Coordinates of the center is

So, the equation of the circle is i.e.

Case 2 :

∴ Coordinates of the center :

So, the equation of the circle is i.e.

Q4. Find the equation of the circle that touches the coordinate axes at the points

and , and the midpoint of chord is .

Answer.

Q5. A circle is inscribed inside a square formed by the lines & .The center of this circle is given by

Answer. Solving,

Solving,

The equation of the sides of the square are . The obtained lines and the inscribed circle can be plotted as:

The Center of the required circle will be the same as the center of the square.

The center of the circle inscribed in the square

Hence, option is the correct answer.

FAQ’s of of Particular cases of a Circle

Question 1. Does the equation of the circle change for different quadrants?

Answer. Yes, since the center of the circle changes the equation will also change but the radius will

remain the same.

Question 2. How many distinct circles passing through three non collinear points are possible?

Answer. Only one circle can be drawn passing through three non collinear points.

Question 3. How many points can lie on a circle?

Answer. Infinite points can lie on a circle.

Question 4.What is the area of the square formed by joining the center of the circles of the same radius and touching the coordinate axes?

Answer. The side of the square will be of length units. Hence, the area of such a square is , where is the radius of the circle

NCERT Class 11 Maths Chapters

Sets	Relations and Functions	Triginometric Functions
Mathematical Induction	Numbers and Quadriatic Equations	Linear Inequalities
Premutations and Combinations	Binomial Theorem	Sequence and Series
Straight Lines	Conic Sections	3 D Geometry
Limits and Derivatives	Mathematical Reasoning	Statistics
Probability