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


Circle Touches y-axis

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

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

If a circle touches the y-axis, then the x-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 - a)\(^{2}\) + (y - k)\(^{2}\) = a\(^{2}\)

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

Hence the equation of the circle is (x - a)\(^{2}\) + (y - k)\(^{2}\) = a\(^{2}\) ⇒ x\(^{2}\) + y\(^{2}\) – 2ax – 2ky + k\(^{2}\) = 0

 

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

1. Find the equation of a circle whose y-coordinate of the centre is -7 and radius is 3 units also touches the y-axis.

Solution:

The required equation of the circle whose y-coordinate of the centre is -7 and radius is 3 units also touches the y-axis is (x - 3)\(^{2}\) + (y + 7)\(^{2}\) = 3\(^{2}\), [Since radius is equal to the x-coordinate of the centre]

⇒ x\(^{2}\) – 6x + 9 + y\(^{2}\) + 14y + 49 = 9

⇒ x\(^{2}\) + y\(^{2}\) - 6x  + 14y + 49 = 0


2. Find the equation of a circle whose radius is 9 units and y-coordinate of the centre is -6 and also touches the y-axis.

Solution:

The required equation of the circle whose radius is 9 units and y-coordinate of the centre is -6 and also touches the x-axis is (x - 9)\(^{2}\) + (y + 6)\(^{2}\) = 9\(^{2}\), [Since radius is equal to the x-coordinate of the centre]

⇒ x\(^{2}\) - 18x + 81 + y\(^{2}\) + 12y + 36 = 81

⇒ x\(^{2}\) + y\(^{2}\) - 18x + 12y + 36 = 0

 The Circle




11 and 12 Grade Math 

From Circle Touches 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. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 09, 25 02:37 AM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More