All grade math formula sheet on co-ordinate geometry. These math formula charts can be used by 10th grade, 11th grade, 12th grade and college grade students to solve co-ordinate geometry.

Co-Ordinate Geometry

x = r cos θ, y = r sin θ

and r = √(x

(ii) The distance between two given points P (x

PQ = √{(x

(iii) Let P (x

(a) If the point R divides the line-segment PQ internally in the ratio m : n, then the co-ordinates of R

are {(mx

(b) If the point R divides the line-segment PQ externally in the ratio m : n, then the co-ordinates of R are

{(mx

(c) If R is the mid-point of the line-segment PQ, then the co-ordinates of R are {(x

(iv) The co-ordinates of the centroid of the triangle formed by joining the points (x

({x

(v) The area of a triangle formed by joining the points (x

½ | y

or, ½ | x

(ii) The slope of x-axis or of a line parallel to x-axis is zero.

(iii) The slope of y-axis or of a line parallel to y-axis is undefined.

(iv) The slope of the line joining the points (x

m = (y

(v) The equation of x-axis is y = 0 and the equation of a line parallel to x-axis is y = b.

(vi) The equation of y-axis is x = 0 and the equation of a line parallel to y-axis is x = a.

(vii) The equation of a straight line in

(a) slope-intercept form: y = mx + c where m is the slope of the line and c is its y-intercept;

(b) point-slope form: y - y

(c) symmetrical form: (x - x

(d) two-point form: (x - x

(e) intercept form:

(f) normal form: x cos α + y sin α = p where p is the perpendicular distance of the line from the origin and α is the angle which the perpendicular line makes with the positive direction of the x-axis.

(g) general form: ax + by + c = 0 where a, b, c are constants and a, b are not both zero.

(viii) The equation of any straight line through the intersection of the lines a

(ix) If p ≠ 0, q ≠ 0, r ≠ 0 are constants then the lines a

(x) If θ be the angle between the lines y= m

(xi) The lines y= m

(a) parallel to each other when m

(b) perpendicular to one another when m

(xii) The equation of any straight line which is

(a) parallel to the line ax + by + c = 0 is ax + by = k where k is an arbitrary constant;

(b) perpendicular to the line ax + by + c = 0 is bx - ay = k

(xiii) The straight lines a

(xiv) The points (x

(xv) Length of the perpendicular from the point (x1, y1) upon the line ax + by + c = 0 is|(ax

(xvi) The equations of the bisectors of the angles between the lines a

(a

The parametric equation of the circle (1) is x = a cos θ, y = a sin θ, θ being the parameter.

(ii) The equation of the circle having centre at (α, β) and radius a units is (x - α)

(iii) The equation of the circle in general form is x

(iv) The equation ax

(v) The equation of a circle concentric with the circle x

(vi) If C

and C

(a) the equation of the circle passing through the points of intersection of C

(b) the equation of the common chord of C

(vii) The equation of the circle with the given points (x

(viii) The point (x

(ii) Other forms of the equations of parabola:

(a) x

Its vertex is the origin and axis is y-axis.

(b) (y - β)

Its vertex is at (α, β) and axis is parallel to x-axis.

(c) (x - α)

Its vertex is at ( a, β) and axis is parallel to y-axis.

(iii) x = ay

(iv) y = px

(v) The parametric equations of the parabola y

(vi) The point (x

x

(a) Its centre is the origin and major and minor axes are along x and y-axes respectively ; length of major axis = 2a and that of minor axis = 2b and eccentricity = e = √[1 – (b

(b) If S and S’ be the two foci and P (x, y) any point on it then SP = a - ex, S’P = a + ex and SP + S’P = 2a.

(c) The point (x

(d) The parametric equations of the ellipse (1) are x = a cos θ, y = b sin θ where θ is the eccentric angle of the point P (x, y) on the ellipse (1) ; (a cos θ, b sin θ) are called the parametric co-ordinates of P.

(e) The equation of auxiliary circle of the ellipse (1) is x

(ii) Other forms of the equations of ellipse:

(a) x

(b) [(x - α)

The centre of this ellipse is at (α, β) and the major and minor ones are parallel to x-axis and y-axis respectively.

(a) Its centre is the origin and transverse and conjugate axes are along x and y-axes respectively ; its length of transverse axis = 2a and that of conjugate axis = 2b and eccentricity = e = √[1 + (b

(b) If S and S’ be the two foci and P (x, y) any point on it then SP = ex - a, S’P = ex + a and S’P - SP = 2a.

(c) The point (x

(d) The parametric equation of the hyperbola (1 ) are x = a sec θ, y = b tan θ and the parametric co-ordinates of any point P on (1) are (a sec θ,b tan θ).

(e) The equation of auxiliary circle of the hyperbola (1) is x

(ii) Other forms of the equations of hyperbola:

(a) y

Its centre is the origin and transverse and conjugate axes are along y and x-axes respectively.

(b) [(x - α)

(iii) Two hyperbolas

x

are conjugate to one another. If e

b

(iv) The equation of rectangular hyperbola is x

(a) circle x

T= xx

(b) circle x

(c) parabola y

(d) ellipse x

where T = (xx

(e) hyperbola x

where T = {(xx

(ii) The equation of the diameter of a conic which bisects all chords parallel to the line y = mx + c is

(a) x + my = 0 when the conic is the circle x

(b) y = 2a/m when the conic is the parabola y

(c) y = - [b

(d) y = [b

(iii) y = mx and y = m’x are two conjugate diameters of the

(a) ellipse x

(b) hyperbola x

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