Is Ellipse part of the EAPCET Mathematics syllabus?

Yes. Ellipse is taught in Intermediate second year · Paper IIB Mathematics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.

How many Mathematics questions are there in EAPCET?

80 of the 160 questions in the Engineering paper are Mathematics, spread across 37 chapters.

What mistakes do students make in Ellipse?

Assuming the major axis is along the x-axis; compare the denominators after making the right side 1. Reading a and b before dividing the equation to get 1 on the right side. Using b² = a²(e² − 1), the hyperbola relation; for an ellipse b² = a²(1 − e²), so e is always less than 1. Taking the latus rectum as 2a²/b; it is 2b²/a, with a the semi-major axis.

EAPCET Mathematics · Intermediate second year · Paper IIB

Ellipse

Ellipse covers the standard ellipse, its eccentricity, foci and directrices, the latus rectum, and tangent conditions.

Subject: Mathematics
Taught in: Intermediate second year · Paper IIB
Mathematics in the paper: 80 of 160 questions

Key formulas and results

$\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1$ $(a > b)$ : $b^{2} = a^{2}(1 - e^{2})$
Foci $(\pm ae, 0)$ and directrices $x = \pm\dfrac{a}{e}$
Latus rectum length $= \dfrac{2b^{2}}{a}$
$y = mx + c$ touches the ellipse iff $c^{2} = a^{2}m^{2} + b^{2}$
Parametric point: $(a\cos\theta, b\sin\theta)$
Sum of the focal distances of any point $= 2a$
Point of contact of the tangent $y = mx + c$ with $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1$ : $\left(-\dfrac{a^{2}m}{c}, \dfrac{b^{2}}{c}\right)$
Area enclosed by the ellipse $\dfrac{x^{2}}{a^{2}} + \dfrac{y^{2}}{b^{2}} = 1$ : $\pi ab$

What this chapter covers

Standard equation
Eccentricity, foci and directrices
Latus rectum
Parametric form
Tangents and normals

How it is usually asked

Find the eccentricity or foci
Write the equation from given data
Apply the tangent condition

Understanding Ellipse

An ellipse is the set of points whose distance from a focus is e times the distance from the matching directrix, with 0 < e < 1. Equivalently, the sum of the distances of any point from the two foci is constant, equal to the length of the major axis. In standard form x²/a² + y²/b² = 1 with a > b, the major axis lies along the x-axis and b² = a²(1 − e²).

From a and e everything else follows. The foci are (±ae, 0), the directrices are x = ±a/e, the vertices are (±a, 0) and the latus rectum has length 2b²/a. If instead b > a, the major axis lies along the y-axis and the roles of a and b swap, so the foci move to the y-axis. Always check which denominator is larger before using any formula.

Points on the ellipse can be written as (a cos θ, b sin θ), which simplifies tangent and normal questions. The line y = mx + c touches the ellipse when c² = a²m² + b², and the tangent at (x₁, y₁) is xx₁/a² + yy₁/b² = 1. EAPCET questions ask for eccentricity, foci, latus rectum, an equation from given data or a tangent condition.

Worked example

EAPCET-style question

The foci of the ellipse $4x^{2} + 3y^{2} = 12$ are

(1) $(\pm 1, 0)$
(2) $(0, \pm 1)$
(3) $(0, \pm 2)$
(4) $(\pm\sqrt{7}, 0)$

Solution

Divide by 12: $\dfrac{x^{2}}{3} + \dfrac{y^{2}}{4} = 1$ .
The larger denominator 4 is under $y^{2}$ , so the major axis is along the $y$ -axis with semi-major axis 2 and semi-minor axis $\sqrt{3}$ .
Distance from centre to each focus $= \sqrt{4 - 3} = 1$ , so $e = \tfrac{1}{2}$ .
The foci are $(0, \pm 1)$ .

Answer: $(0, \pm 1)$

Common mistakes to avoid

Assuming the major axis is along the x-axis; compare the denominators after making the right side 1.
Reading a and b before dividing the equation to get 1 on the right side.
Using b² = a²(e² − 1), the hyperbola relation; for an ellipse b² = a²(1 − e²), so e is always less than 1.
Taking the latus rectum as 2a²/b; it is 2b²/a, with a the semi-major axis.

How to prepare it

Check whether the major axis is along x or y before using any formula.

Once the formulas feel familiar, test them the way the exam does: practise Ellipse questions chapter-wise, then attempt a full previous year paper to see whether it holds up under a 3-hour timer.

Related Mathematics chapters

See every chapter in the EAPCET Mathematics syllabus.

Practise Ellipse chapter-wise

Chapter-wise quizzes show exactly which topics in this chapter you still get wrong — before a full paper does.

Frequently asked questions

Is Ellipse part of the EAPCET Mathematics syllabus?: Yes. Ellipse is taught in Intermediate second year · Paper IIB Mathematics, and the EAPCET Engineering syllabus is based on the Intermediate first- and second-year syllabus. Check the official notification each year for any changes.
How should I prepare Ellipse for EAPCET?: Check whether the major axis is along x or y before using any formula.
How many Mathematics questions are there in EAPCET?: 80 of the 160 questions in the Engineering paper are Mathematics, spread across 37 chapters.
What mistakes do students make in Ellipse?: Assuming the major axis is along the x-axis; compare the denominators after making the right side 1. Reading a and b before dividing the equation to get 1 on the right side. Using b² = a²(e² − 1), the hyperbola relation; for an ellipse b² = a²(1 − e²), so e is always less than 1. Taking the latus rectum as 2a²/b; it is 2b²/a, with a the semi-major axis.