Excel in the concepts of coordinate geometry by knowing everything from important topics, preparation tips and formulas to practical applications. Read the complete article to know more:

1. Coordinate Geometry

2. Coordinate geometry is one of the most interesting and
important topics of the mathematics syllabus of JEE
Advanced and JEE Main. It is one of the easiest and most
scoring topic of JEE mathematics. The applications of
coordinate geometry are spread through various fields of
mathematics like trigonometry, calculus, dimensional
geometry etc. and also have application in statistics and
physics.

3. Important topics in coordinate geometry for IIT JEE
We shall give a brief introduction of each of these sub – topics along with the
tips to master them. Beginners are advised to refer the study material on
coordinate geometry.

4. Important concepts and formulae
Distance Formula
Distance ‘d’ between any two points A (x1,y1) and B (x2,y2) on the coordinate
axis is given by

5. Section Formula
Coordinates of P when it divides the line AB in the ratio m : n
Area of triangle
There are many formulas for area of triangle. Basically it depend on
what we have given in the question.
• Case I: If height ‘h’ and base ‘b’ are given. Then area ‘A’ is
• Case II: If coordinates of points are given. Let say A(x1, y1), B(x2,y2 ) and
C(x3,y3 ). Then area ‘A’ is

6. Equation of straight line
• Point – Slope form
• Point – Point form
• Slope intercept form
• Intercept form
• Normal form

7. Distance of a point from a line
Line: ax+by+c=0. Let the point be P(x1,y1). Then distance ‘d’ of the
point P from the line is
Distance between two parallel lines
Line 1: ax+by+c=0, Line 2: ax+by+c’=0.Then distance ‘d’ between
lines is

8. Concurrency of lines
Two lines are always concurrent if they are not parallel. Three lines
a1x+b1y+c1=0 , a2x+b2y+c2=0 , a3x+b3y+c3=0 are concurrent if
Colinearity of points
Three points A(x1,y1), B(x2,y2) and C(x3,y3)are collinear if

9. Angle between two lines
Let the slope of two lines be m1 and m2. Then angle between two lines is
Position of point w.r.t line
Position of point A(x1,y1) and B(x2,y2) w.r.t line ax+by+c=0.
If ax1+by1+c1=0 and ax2+by2+c2=0 are of same sign, then points A and B lie on
the same side of the line and if they are of opposite sign, then they lie on the
opposite side of line.
Locus
Locus is a path trace by a moving or a variable point under certain given
condition. If we find the equation of traced path, then the equation is the
required locus. Steps to follow:
 Assume point (h, k) whose locus is to find
 Use the given condition
 Remove the variable
 After removing the variable, equation will be left in h, k and some fixed
number. Finally replace ‘h’ by ‘x’ and ‘k’ by ‘y’ to get the required locus.

10. CONIC SECTION

11. Circle

12. Parabola

13. Ellipse

14. Hyperbola

15. Is coordinate geometry an important part of IIT – JEE
preparation?
Coordinate geometry is an important part of JEE maths paper. It can
really improve your rank. Each year in the JEE mathematics, we have
around 20% - 25% of the total marks of mathematics from this part.
Among the coordinate geometry, almost 50% of the total question
cover from the straight line and the circles.
Books to Refer
 Coordinate Geometry by SL Loney
 Arihant Coordinate Geometry
 Tata Mcgraw Hill for IIT – JEE

16. Some Interesting Facts
 The locus of a point from which the distance of two tangents to a circle are
equal is radical axis.
 Minimum distance between any two curves always lies along the normal.
 PQ be the focal chord of parabola and S be the focus of the parabola. Then,
SP, 2a and SQ are in Harmonic progression.
 Tangents at the extremities of the focal chord intersect at right angle on
the directrix.
 Locus of all those points which divide the perpendicular drawn from any point
on the circle to any one of the fixed diameter in a constant ratio is an ellipse.
 Auxiliary circle is a circle concentric with the ellipse and having diameter
equal to the major axis of the ellipse.
 Maximum four normals can be drawn to ellipse.

17. Tips to study Coordinate Geometry
 Do not practice a single problem in coordinate geometry without drawing a
figure.
 Important results should be on your tips which might prove helpful in many
of the objective problems.
 Make a different notebook for the formulas. Write all the important
formulas in your notebook on daily basis.
 Try to memorize as much formulae as you can.
 Read the question clearly to figure out what it actually demands. It might
save your time.
 Practice as many problems as you can from the reference books. Then try
to solve the previous year JEE paper problems of coordinate geometry.
 Try your level best to solve a problem before referring its solution.

18. Practical Applications
 Coordinate geometry is used in astronomy particularly in computing the
paths of celestial bodies like planets, comets, binary star system etc.
 Coordinate geometry is used in the study of the paths of projectile like
missile and other arms.
 Coordinate geometry is extremely useful in the aircraft industry,
specifically when dealing with the shape of an airplane's fuselage.
 Computer programmers use coordinate geometry because most of the
program they write generate PDF files. And in a PDF file the printed page is
one big coordinate plane.
 Coordinate geometry is also used in the scanners. Scanner make use of the
coordinate geometry to reproduce the exact image of the selected picture
in the computer. It manipulates the points of each information in the
original documents.

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