Conic Sections Class 11 Formulas
Conic sections class 11 formulas introduce students to ellipses, parabolas and hyperbolas. The knowledge of these formulas is quite helpful for students to solve various problems in mathematics as well as in other subjects like physics. Thus, it is highly imperative that students must possess a clear understanding of all basic concepts and terms used in these formulas.
List of Conic Sections Class 11 Formulas
Students can refer to the list of conic sections class 11 formulas provided below to understand all relevant concepts.
- Standard Equation of Circle: For C (h, k) as the center and ‘r’ as the radius of a circle, (x – h)2 + (y – k)2 = r2 where P(x, y) is any point on the circle
- Standard Equation of Ellipse: x2/a2 + y2/b2 = 1 where origin is the center of the ellipse and ‘a’ and ‘b’ are the X and Y intercepts respectively.
- Equation of hyperbola with foci on x-axis: x2/a2 - y2/b2 = 1 where center lies on the origin, ‘a’ is the distance from center to the vertex, ‘c’ is the distance from center to foci; b2 = c2 - a2
- Length of the latus rectum of the ellipse: x2/a2 + y2/b2 = 1 is 2b2/a
Applications of Conic Sections Class 11 Formulas
The conic sections class 11 formulas have their applications in several areas. Some of these are listed below:
- Curves play an important role in designing applications to explore space and also to study the behavior of atomic particles. Therefore, conic sections class 11 formulas are widely applied in the field of space science.
- Conic formulas help in determining important information in many practical scenarios such as planetary motion, design of antennas and telescopes, automobile headlights and reflectors in flashlights.
Tips to Memorize Conic Sections Class 11 Formulas
Conic Sections class 11 formulas introduce a lot of new terminologies that students should be aware of in order to remember them. Here are some useful tips that students can follow to memorize these formulas better:
- Students can grasp these formulas better through visual resources like explanatory videos with simulations. Learning through such resources will help students to memorize the details of the formulas.
- The solved examples in the textbooks can be very helpful in learning the facts, so students should make read and practice all of them.
- Students can use math apps or interactive worksheets to practice and learn the formulas. It will help them quickly revise these formulas whenever they want.
Conic Sections Class 11 Formulas Examples
Example 1: What is the equation of a circle whose center is at (4,3) and radius equal to 5?
Solution : Using the formula , (x2 - h2) + (y2 - k2) = r2
Substituting values of (h, k) as (4, 3) and r as 5 we get,
= x2 - 16 + y2 - 9 = 25
= x2 + y2 - 25 = 25
= x2 + y2 = 50
Therefore, the equation of the circle is x2 + y2 = 50.
Example 2: What is the equation of a parabola with vertex at origin i.e. (0, 0) and focus point as (0, 3)?
Solution : Vertex of parabola = (0, 0) and Focal point of this parabola = (0, 3)
Since it lies on Y-axis, the axis of this parabola is Y-axis
By using the formula, x2 = 4ay, we get x2 = 4(3)y
= x2 = 12y
Hence, the equation of the parabola is x2 = 12y.
Students can download the printable Maths Class Formulas 11 sheet from below.
FAQs on Conic Sections Class 11 Formulas
What are the Important Formulas for Conic Sections Class 11 Formulas?
- Standard Equation of Circle: For C (h, k) as the center and ‘r’ as the radius of a circle, (x – h) 2 + (y – k) 2 = r 2 where P(x, y) is any point on the circle
- Standard Equation of Ellipse: x2/a2 + y2/b2 = 1 where origin is the center of the ellipse and ‘a’ and ‘b’ are the X and Y intercepts respectively.
- Equation of hyperbola with foci on x-axis: x2/a2 - y2/b2 = 1 where center lies on the origin, ‘a’ is the distance from center to the vertex, ‘c’ is the distance from center to foci; b2 = c2 - a2
- Length of the latus rectum of the ellipse: x2/a2 + y2/b2 = 1 is 2b2/a
What are the Basic Concepts Used in Conic Sections Class 11 Formulas?
The basic concepts used in Conic Sections Class 11 Formulas are related to the equations of ellipse, equation of circle with given points as center, hyperbolas, and length of the latus rectum of the ellipse. The understanding of these concepts is helpful in mathematics and other domains such as physics. Hence, it is important to follow up with these formulas and concepts thoroughly.
What is it Important to Practice Problems Based on Conic Sections Class 11 Formulas?
Practicing problems based on Conic Sections Class 11 Formulas provides an In-depth knowledge of the different curves and their equations along with various terms related to them like the latus rectum and eccentricity.
How Many Formulas are there in Conic Sections Class 11 Formulas?
There are four major conic sections class 11 formulas that cover the topics of standard equations of circle, parabola, ellipse, hyperbola, conic sections. Students should also revise the relationship between semi-major axis, semi-minor axis, and the special cases of the ellipse. Concepts of eccentricity and latus rectum are also important.
How can I Memorize Conic Sections Class 11 Formulas?
Some useful tips that can help students in memorizing conic sections class 11 formulas are as follows:
- Visualization of formulas through formula diagrams will help in building a logical understanding of them.
- Understanding steps in formulas derivations provided will help form a clear understanding of these formulas.
- Applying formulas in solving a variety of problems will help students get well versed in them.