Coordinate Geometry is a simple method
of analyzing geometrical shapes. It is one of the most scoring topics of
IIT JEE Math course. After calculus, it is the only syllabus that can get you
full marks. The topic covers:
 Straight Lines
 Hyperbola
 Ellipse
 Parabola
 Circle
· If ABCD is a
parallelogram, then D= AB+C
· Area of Rhombus framed by ax (+ or ) by (+or ) c = 0 is calculated by 2c^{2}/ab
· The equation of line parallel to X axis is form = k
· If a line slope passes through (x1, y1) and (x2, y2) is (y2y1)(x2x1) only when x1is not equal to x2
· The equation of a line running parallel to x axis is of the form y=k
· The equation of a line with m slope and intercept y is y= mx+c
· The equation of line for non zero intercept and b on x and y axis is (x/a) + (y/b)= 1
· The intersection point of two lines, that don’t run parallel can be detected by solving them simultaneously
· ax+ by + c= 0
· y= mx +b where m= slope and b =y – intercept
· y y1 = m (x x1), where m= slope and the lines passes via (x1, y1)
· Three points X Y and Z are collinear if (slope (xy) = Slope (yz). This is the right collinearity test
· Area of Rhombus framed by ax (+ or ) by (+or ) c = 0 is calculated by 2c^{2}/ab
· The equation of line parallel to X axis is form = k
· If a line slope passes through (x1, y1) and (x2, y2) is (y2y1)(x2x1) only when x1is not equal to x2
· The equation of a line running parallel to x axis is of the form y=k
· The equation of a line with m slope and intercept y is y= mx+c
· The equation of line for non zero intercept and b on x and y axis is (x/a) + (y/b)= 1
· The intersection point of two lines, that don’t run parallel can be detected by solving them simultaneously
· ax+ by + c= 0
· y= mx +b where m= slope and b =y – intercept
· y y1 = m (x x1), where m= slope and the lines passes via (x1, y1)
· Three points X Y and Z are collinear if (slope (xy) = Slope (yz). This is the right collinearity test
1. Tangents are drawn to the circle x^2 + y^2=12 at
the points where it is met by the circle x^2 +y^2  5x + 3y  2=0.Find the
point of intersection of these tangents
Solve
both the equations for x as well as y
Method:
x^2 +
y^2=12
When
you put this in the second equation, you get 5x +3y =10, thus, x= (3y +10)/5
So
[(3y+10)/5]^{2 }+ y^{2} = 12. Now get y and find x and
eventually you will get first circle tangent and then intersection points of
the tangents
2.
Slope of a Line
The tangent of
angle made by a line with positive in clockwise direction is said to be the
slope of the line which is marked by letter m.
If (x1, y1) and
(x2, y2) are two points on a line, you can find the slope as slope(m)= (y2y1)/
(x2x1)
3. Conditions for Two Lines to be Parallel or
Perpendicular
Two lines with slopes supposedly,
m1 and m2:
they would be parallel if m1=m2
they will be perpendicular if m1 . m2 = 1
they would be parallel if m1=m2
they will be perpendicular if m1 . m2 = 1
4. How to identify Slope, XIntercept, YIntercept
from an equation of a line
The given equation is ax+by+c=0
>m=a/b
>xintercept=c/a
>yintercept=c/b
>m=a/b
>xintercept=c/a
>yintercept=c/b
5. A line crosses via (2,2) and stands perpendicular to 3x+y = 3. What is
the –intercept of the line
Slope
of the line = 1 /slope of 3x+y= 3
Thus
the Slope is 1/3
The
equation formed is y – 2/ x 2 = 1/3
In
other words, x 3y +4 = 0
Thus, Y
intercept is 4/3
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