When exams are round the corner then it is not possible to revise complete books so we have come up with unit wise formulas and important terms. Once you have gone through chapters thoroughly and understood it well there is no need to study it again and again. You can only revise important formulas and terms which will save your precious time.
Find revision notes for unit Coordinate Geometry-I in this article. This unit includes chapters – Straight lines and Circles. All formulae and important terms from these chapters are covered in this revision notes. In UPSEE and WBJEE where most of questions are asked directly on formulae, this quick revision note is very important.
- Distance between the points P (x1, y1) and Q (x2, y2) is
- The coordinates of a point dividing the line segment joining the points (x1, y1) and
Q (x2, y2) internally, in the ratio m: n are
- Area of the triangle whose vertices are (x1, y1), (x2, y2)and Q (x3, y3) is
- The angle (say) θ made by the line l with positive direction of x-axis and measured anti clockwise is called the inclination of the line and tan θ is called the slope of line, denoted by m.
- Two non vertical lines l1 and l2 are parallel if and only if their slopes are equal.
- Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other
- The acute angle (say θ) between lines L1 and L2 with slopes m1 and m2, respectively, is given by
- If two lines having the same slope pass through a common point, then two lines will coincide.
- Equation of a horizontal line line L is either y = a or y = −a
- Equation of a vertical line at a distance b from the y-axis is either x = b or x = −b
- Point-slope form of a line
The equation of a line passing through point (x, y) and have slope m is
- Two-point form of line
The equation of a line passing through points (x1, y1) and (x2, y2) is
- Slope-intercept form of line
The equation of a line with slope m and c as y-intercept is
y = mx + c
- Intercept form of a line
The equation of the line making intercepts a and b on x-and y-axis, respectively, is
- Normal form of a line
The equation of the line having normal distance p from the origin and angle θ which the normal makes with the positive direction of x-axis is given by
x cosθ + y sinθ = p
- The perpendicular distance (d) of a line Ax + By+ C = 0 from a point (x1, y1) is given by
- The distance d between two parallel lines y = mx + c1 and y = mx + c2 is
- A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.
- The fixed point is called the centre of the circle.
- The distance from the centre to a point on the circle is called the radius of the circle.
The required equation of the circle with centre at (h, k) and radius r is
(x – h)2 + (y – k)2 = r2