Processing math: 100%

Subscribe to our YouTube channel for the latest videos, updates, and tips.


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 = a2.

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

Then the equation (x - h)2 + (y - k)2 = a2 becomes x2 + (y - k)2 = a2 ⇒ x2 + y2 - 2ky + k2 = a2 ⇒ x2 + y2 - 2ky + k2 - a2 = 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

x2 + (y + 3)2 = 62

⇒ x2 + y2 + 6y + 9 = 36

⇒ x2 + y2 + 6y + 9 - 36 = 0

⇒ x2 + y2 + 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

x2 + (y - 4)2 = 42

⇒ x2 + y2 - 8y + 16 = 16

⇒ x2 + y2 – 8y + 16 - 16 = 0

⇒ x2 + y2 - 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. Worksheet on Average | Word Problem on Average | Questions on Average

    May 19, 25 02:53 PM

    Worksheet on Average
    In worksheet on average we will solve different types of questions on the concept of average, calculating the average of the given quantities and application of average in different problems.

    Read More

  2. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More