Centre of the Circle on y-axis

We will learn how to find the equation when the centre of a circle on y-axis.

The equation of a circle with centre at (h, k) and radius equal to a, is (x - h)\(^{2}\) + (y - k)\(^{2}\) = a\(^{2}\).

When the centre of a circle is on the y-axis i.e., h = 0.

Then the equation (x - h)\(^{2}\) + (y - k)\(^{2}\) = a\(^{2}\) becomes x\(^{2}\) + (y - k)\(^{2}\) = a\(^{2}\) β‡’ x\(^{2}\) + y\(^{2}\) - 2ky + k\(^{2}\) = a\(^{2}\) β‡’ x\(^{2}\) + y\(^{2}\) - 2ky + k\(^{2}\) - a\(^{2}\) = 0

If the centre of a circle be on the y-axis, then the x co-ordinate of the centre will be zero. Hence, the general form of the equation of the circle will be of the form x2 + y2 + 2fy + c = 0, where g and c are the constants.

Solved examples on the central form of the equation of a circle whose centre is on the y-axis:

1. Find the equation of a circle whose centre of a circle is on the y-axis at -3 and radius is 6 units.

Solution:

Radius of the circle = 6 units.

Since, centre of a circle be on the y-axis, then the x co-ordinate of the centre will be zero.

The required equation of the circle whose centre of a circle is on the y-axis at -3 and radius is 6 units is

x\(^{2}\) + (y + 3)\(^{2}\) = 6\(^{2}\)

β‡’ x\(^{2}\) + y\(^{2}\) + 6y + 9 = 36

β‡’ x\(^{2}\) + y\(^{2}\) + 6y + 9 - 36 = 0

β‡’ x\(^{2}\) + y\(^{2}\) + 6y - 27 = 0


2. Find the equation of a circle whose centre of a circle is on the y-axis at 4 and radius is 4 units.

Solution:

Radius of the circle = 4 units.

Since, centre of a circle be on the y-axis, then the x co-ordinate of the centre will be zero.

The required equation of the circle whose centre of a circle is on the y-axis at 4 and radius is 4 units is

x\(^{2}\) + (y - 4)\(^{2}\) = 4\(^{2}\)

β‡’ x\(^{2}\) + y\(^{2}\) - 8y + 16 = 16

β‡’ x\(^{2}\) + y\(^{2}\) – 8y + 16 - 16 = 0

β‡’ x\(^{2}\) + y\(^{2}\) - 8y = 0

● The Circle






11 and 12 Grade Math 

From Centre of the Circle on y-axis to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 16, 25 02:45 AM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  2. Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples

    Jul 16, 25 02:33 AM

    Perimeter of a Figure
    Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav…

    Read More

  3. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 15, 25 11:46 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

  4. 5th Grade Quadrilaterals | Square | Rectangle | Parallelogram |Rhombus

    Jul 15, 25 02:01 AM

    Square
    Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example:

    Read More

  5. 5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans

    Jul 14, 25 01:53 AM

    Name the Angles
    In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…

    Read More