Is Locus part of the EAPCET Mathematics syllabus?

Yes. Locus is taught in Intermediate first year · Paper IB 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 Locus?

Squaring PA = 2PB as PA² = 2PB²; the factor must be squared too, giving PA² = 4PB². Leaving the final answer in h and k instead of replacing them with x and y. Substituting back before the parameter has been eliminated, which leaves an equation that still depends on it. Using the coordinates of the fixed point instead of the moving point when applying the condition, which gives a single point instead of a curve.

EAPCET Mathematics · Intermediate first year · Paper IB

Locus

Locus is the set of all points that satisfy a condition. The chapter teaches how to turn a geometric condition into an equation in x and y.

Subject: Mathematics
Taught in: Intermediate first year · Paper IB
Mathematics in the paper: 80 of 160 questions

Key formulas and results

Distance between $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ $= \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
Points equidistant from two fixed points lie on the perpendicular bisector of the segment joining them.
Points at a fixed distance from a fixed point lie on a circle.
Section formula: $\left(\dfrac{mx_{2} + nx_{1}}{m + n}, \dfrac{my_{2} + ny_{1}}{m + n}\right)$

What this chapter covers

Definition of a locus
Finding the equation of a locus
Loci defined by distances and ratios

How it is usually asked

Find the locus of a point satisfying a distance condition
Find the locus of a midpoint or centroid as a point moves

Understanding Locus

A locus is the path traced by a point that moves so that it always satisfies a given condition. The condition may be about distances from fixed points or lines, about ratios, about angles, or about the point being the midpoint or centroid of some moving figure. The equation of the locus is an equation in x and y that every such point satisfies and no other point does.

The standard method has three steps. Let the moving point be P(h, k). Write the given condition as an equation in h and k, using the distance formula, section formula or slope as needed, and remove any parameter that appears. Finally replace h by x and k by y. Squaring both sides of a distance condition early removes square roots and keeps the algebra simple.

Familiar loci help you check answers: points equidistant from two fixed points form the perpendicular bisector, points at a fixed distance from a fixed point form a circle, and points whose distances from two fixed points are in a fixed ratio other than 1 also form a circle. EAPCET questions on this chapter are short derivations of such equations.

Worked example

EAPCET-style question

A point $P$ moves so that its distance from $A(2, 0)$ is twice its distance from $B(-1, 0)$ . The locus of $P$ is

(1) $x^{2} + y^{2} + 4x = 0$
(2) $x^{2} + y^{2} - 4x = 0$
(3) $x^{2} + y^{2} + 4x + 4 = 0$
(4) $3x^{2} + 3y^{2} - 12x + 8 = 0$

Solution

Let $P = (h, k)$ . The condition $PA = 2PB$ gives $PA^{2} = 4PB^{2}$ .
$(h - 2)^{2} + k^{2} = 4[(h + 1)^{2} + k^{2}]$ .
Expand: $h^{2} - 4h + 4 + k^{2} = 4h^{2} + 8h + 4 + 4k^{2}$ , so $3h^{2} + 3k^{2} + 12h = 0$ .
Divide by 3 and replace $h, k$ by $x, y$ : $x^{2} + y^{2} + 4x = 0$ .
Check: the origin is at distance 2 from $A$ and 1 from $B$ , and it satisfies the equation.

Answer: $x^{2} + y^{2} + 4x = 0$

Common mistakes to avoid

Squaring PA = 2PB as PA² = 2PB²; the factor must be squared too, giving PA² = 4PB².
Leaving the final answer in h and k instead of replacing them with x and y.
Substituting back before the parameter has been eliminated, which leaves an equation that still depends on it.
Using the coordinates of the fixed point instead of the moving point when applying the condition, which gives a single point instead of a curve.

How to prepare it

Call the moving point (h, k), write the condition, then replace h, k by x, y at the end.

Eliminate any parameter before you substitute back.

Once the formulas feel familiar, test them the way the exam does: practise Locus 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 Locus 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 Locus part of the EAPCET Mathematics syllabus?: Yes. Locus is taught in Intermediate first year · Paper IB 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 Locus for EAPCET?: Call the moving point (h, k), write the condition, then replace h, k by x, y at the end. Eliminate any parameter before you substitute back.
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 Locus?: Squaring PA = 2PB as PA² = 2PB²; the factor must be squared too, giving PA² = 4PB². Leaving the final answer in h and k instead of replacing them with x and y. Substituting back before the parameter has been eliminated, which leaves an equation that still depends on it. Using the coordinates of the fixed point instead of the moving point when applying the condition, which gives a single point instead of a curve.