# Circle Touches x-axis

We will learn how to find the equation of a circle touches x-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 circle touches x-axis i.e., k = a.

Then the equation (x - h)$$^{2}$$ + (y - k)$$^{2}$$ = a$$^{2}$$ becomes  (x- h)$$^{2}$$ + (y - a)$$^{2}$$ = a$$^{2}$$

If a circle touches the x-axis, then the y-co-ordinate of the centre will be equal to the radius of the circle. Hence, the equation of the circle will be of the form

(x - h)$$^{2}$$ + (y - a)$$^{2}$$ = a$$^{2}$$

Let C (h, k) be the centre of the circle. Since the circle touches the x-axis, therefore, a = k

Hence the equation of the circle is (x - h)$$^{2}$$ + (y - a)$$^{2}$$ = a$$^{2}$$ ⇒ x$$^{2}$$ + y$$^{2}$$ - 2hx - 2ay + h$$^{2}$$ = 0

Solved examples on the central form of the equation of a circle touches x-axis:

1. Find the equation of a circle whose x-coordinate of the centre is 5 and radius is 4 units also touches the x-axis.

Solution:

The required equation of the circle whose x-coordinate of the centre is 5 and radius is 4 units also touches the x-axis is (x - 5)$$^{2}$$ + (y - 4)$$^{2}$$ = 4$$^{2}$$, [Since radius is equal to the y-coordinate of the centre]

⇒ x$$^{2}$$ – 10x + 25 + y$$^{2}$$ – 8y + 16 = 16

⇒ x$$^{2}$$ + y$$^{2}$$ - 10x - 8y + 25 = 0

2. Find the equation of a circle whose radius is 7 units and x-coordinate of the centre is -2 and also touches the x-axis.

Solution:

The required equation of the circle whose radius is 7 units and x-coordinate of the centre is -2 and also touches the x-axis is (x + 2)$$^{2}$$ + (y - 7)$$^{2}$$ = 7$$^{2}$$, [Since radius is equal to the y-coordinate of the centre]

⇒ x$$^{2}$$ + 4x + 4 + y$$^{2}$$ – 14y + 49 = 49

⇒ x$$^{2}$$ + y$$^{2}$$ + 4x - 14y + 4 = 0

The Circle

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.

## Recent Articles

1. ### Method of L.C.M. | Finding L.C.M. | Smallest Common Multiple | Common

Apr 15, 24 01:29 AM

We will discuss here about the method of l.c.m. (least common multiple). Let us consider the numbers 8, 12 and 16. Multiples of 8 are → 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ......

2. ### Common Multiples | How to Find Common Multiples of Two Numbers?

Apr 15, 24 01:13 AM

Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24…

3. ### Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

Apr 14, 24 03:06 PM

The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is t…

4. ### Worksheet on H.C.F. | Word Problems on H.C.F. | H.C.F. Worksheet | Ans

Apr 14, 24 02:23 PM

Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers…