Geometry- Preparation Tips to Practical Applications! - askIITians

1
Coordinate Geometry
2
IIT JEE Coordinate Geometry- Preparation Tips

• 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 axbyc0. 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 axbyc0, Line 2 axbyc0.Then
  distance d between lines is

8

• Concurrency of lines
• Two lines are always concurrent if they are
  not parallel. Three lines
• a1xb1yc10 ,  a2xb2yc20
   , a3xb3yc30 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 axbyc0.
• If ax1by1c10 and ax2by2c20 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.

19
Free Coaching Consultation

• For a free demo class or consultation, please
  contact
• Email info_at_askIITians.com
• Call us at 18002000838
• Visit www.askIITians.com