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 – x₀)² + (y – y₀)² = r².
• For circle x² + y² = a², the equation of the chord is x₁x + y₁y = a²
• The equation of the chord of the circle x² + y² + 2gx + 2fy + c = 0 with M(x₁, y₁) as the midpoint of the chord is given by: xx₁ + yy₁ + g(x + x₁) + f(y + y₁) = x₁² + y₁² + 2gx₁ + 2fy₁ i.e. T = S₁.

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 = r².

(x - 3)² + (y - 2)² = 5²

(x² - 3x + 9) + (y² − 4y + 4) = 25

X² + y² - 2x - 4y - 11 = 0

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