The set of all points on a plane whose distance from two points add up to a constant is called an ellipse. It is an important topic in the conic section. These fixed points are called foci. The centre is the midpoint of the line segment joining the foci. The major axis is the line segment passing through the foci. Students can expect 1-2 questions from the conic section for the JEE Main exam.
In this article, we come across a type of conic section and important previous year questions.
The line segment passing through the centre and perpendicular to the major axis is called the minor axis. The endpoints of the major axis are called the vertices of the ellipse. The distance between the foci is denoted by 2c. So the length of the semi-major axis is a and the semi-minor axis is b. The length of the major axis is denoted by 2a and the minor axis is denoted by 2b.
Standard Equation Of Ellipse
The standard equation is given by (x2/a2) + (y2/b2) = 1.
Here a and b are the length of the semi-major axis and the semi-minor axis respectively. The foci will lie on the major axis. We can find the major by finding the intercepts on the axes of symmetry, i.e, if the coefficient of x2 has the larger denominator then the major axis is along the x-axis and it is along the y-axis if the coefficient of y2 has the larger denominator.
How to Find the Equation
- Find the axis of the major axis.
- If the vertices are (±a, 0) and foci are (±c, 0), then the major axis is parallel to the x-axis. Then the equation is (x2/a2) + (y2/b2) = 1.
- If the vertices are (0, ±a) and foci are (0,±c), then the major axis is parallel to the y-axis. Then the equation is (x2/b2) + (y2/a2) = 1.
- Use c2 = (a2 – b2), to find b2.
- Put the values of a2 and b2 in the standard form.
It is the chord through one focus and perpendicular to the major axis or parallel to the directrix. It is a double ordinate passing through the focus. The equation of the latus rectum is given by 2b2/a.
Area Of Ellipse
The area is given by πab. Here a and b are the length of the semi-major axis and the semi-minor axis respectively.
- Length of major axis = 2a
- Length of minor axis = 2b
- Latus rectum length = 2b2/a
- Area = πab
- Centre = C(0,0)
- Circumference = π√(2(a2+b2))
Conic Sections Previous Year Questions With Solutions
Conic section is an important topic for the JEE exam. Students are recommended to learn JEE Main Conic Sections previous year questions with solutions. These solutions will help students to understand the pattern of questions asked for the JEE Main exam. Students can easily access these solutions and download them in PDF format from the website.
All the solutions are prepared by subject matter experts. Practising previous year question papers help students to improve their speed and accuracy. This helps students to be stress-free and confident during the exam.