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# Circles Formulas Class 12

Circles formulas class 12 maths are highly important for competitive exams preparation. A circle is the locus of points that moves in a plane such that its distance from a fixed point is always constant. The fixed point is known as the center of the circle while the fixed distance is called the ‘radius’. This article will help you to have a clear idea of the important circle formulas including the equation of tangent, normal and chord of contact.

## List of Circles Formulas Class 12

- Equation of a circle with center at C(x0, y0) and radius r is (x – x
_{0})^{2}+ (y – y_{0})^{2}= r^{2}. - For circle x
^{2}+ y^{2}= a^{2}, the equation of the chord is x_{1}x + y_{1}y = a^{2} - The equation of the chord of the circle x
^{2}+ y^{2}+ 2gx + 2fy + c = 0 with M(x_{1}, y_{1}) as the midpoint of the chord is given by: xx_{1}+ yy_{1}+ g(x + x_{1}) + f(y + y_{1}) = x_{1}^{2}+ y_{1}^{2}+ 2gx_{1}+ 2fy_{1}i.e. T = S_{1}.

## Applications of Circles Formulas Class 12

Some of the basic applications of circles formulas class 12 are listed below:

- The use of the circle formulas class 12 is quite prevalent in many fields including engineering, architecture, navigation etc. These formulas are often used in making watches, clocks, bicycles, cars, trains, ships, airplanes, radios, telephones, trolleys, wheel-barrows, air-conditioners, rockets etc.
- Important information related to various real-life situations can be determined by using circle formulas related to the radius, parameters. For example, knowing the circumference of the planets helps us compare their relative sizes, and artificial satellites that are launched travel in orbits of certain circumference.

## Tips to Memorize Circles Formulas Class 12

Here are some helpful tips for students to easily memorize circle formulas class 12:

- The students must make sure to understand the concepts first before moving ahead to memorize the formulas. They can get help from teachers or their friends to get clarity on the same.
- They can also go through the derivation of these formulas to develop a rock-solid foundation as well as understand the underlying concepts.
- It is necessary that the students must practice a variety of questions based on median formulas to ensure a conceptual understanding of all important formulas.

## Examples of Circles Formulas Class 12

**Example:** Write the equation of a circle with the center at O(3,2) and radius 5.

**Solution:**

As we know that the equation of a circle with a center at O(x0, y0) and radius r is (x – x0)^{2} + (y – y0)^{2} = r^{2}.

(x - 3)^{2} + (y - 2)^{2} = 5^{2}

(x^{2} - 3x + 9) + (y^{2} − 4y + 4) = 25

X^{2} + y^{2} - 2x - 4y - 11 = 0

Students can download the printable** Maths Formulas Class 12** sheet from below.

## FAQs On Circles Formulas Class 12

### What are the Most Important Circles Formulas Class 12?

Some of the most important formulas covered under Circles Formulas Class 12 are:

- Equation of a circle with center at C(x
_{0}, y_{0}) and radius r is (x – x_{0})^{2}+ (y – y_{0})^{2}= r^{2}. - For circle x
^{2}+ y^{2}= a^{2}, the equation of the chord is x_{1}x + y_{1}y = a^{2} - The equation of the chord of the circle x
^{2}+ y^{2}+ 2gx + 2fy + c = 0 with M(x_{1}, y_{1}) as the midpoint of the chord is given by: xx_{1}+ yy_{1}+ g(x + x_{1}) + f(y + y_{1}) = x_{1}^{2}+ y_{1}^{2}+ 2gx_{1}+ 2fy_{1}i.e. T = S_{1}.

### Why is it Important to Solve Problems Based on Circles Formulas Class 12?

Solving multiple problems based on Circles Formulas Class 12 will enable students to enhance their understanding of concepts related to this topic and their applications. Students can develop discreet problem-solving skills with the regular practice of questions based on circle formulas. It also helps students in the preparation for exams.

### How Many Circles Formulas are there?

There are around 4 main Circles Formulas. Students should thoroughly understand each and every one of them along with the practice problems based on them. A clear understanding of the terms and concepts related to Circles Formulas Class 12 will be helpful in solving a variety of problems from this topic.

### How to Download the Circles Formulas Class 12 pdf?

Students can download the Circles Formulas Class 12 pdf through the option provided on this page. Enter your phone number to receive OTP. Provide the OTP to automatically download the formula sheet on your device.

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