IIT JEE Coordinate Geometry- Preparation Tips to Practical Applications! - askIITians

Coordinate Geometry

IIT JEE Coordinate Geometry- Preparation TipsCoordinate 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.

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.

Important concepts and formulaeDistance Formula

Distance ‘d’ between any two points A (x1,y1) and B (x2,y2) on the coordinate axis is given by

Section FormulaCoordinates 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

Equation of straight line• Point – Slope form

• Point – Point form

• Slope intercept form

• Intercept form

• Normal form

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

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

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. 

CONIC SECTION

Circle

Parabola

Ellipse

Hyperbola

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

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.

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.

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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