math_coordinate_geometryCoordinate geometry
Distance formulaL=(x1-x2)2+(y1-y2)2
Slope of a line when coordinates of any two points on the line are givenslope=m=y2-y1x2-x1
Two lines with slope m1andm2 are parallel if m1=m2
Two lines with slope m1andm2 are perpendicular if m1.m2=-1
Angle between two lines with slope m1andm2 tanπœƒ=m2-m11+m1m2
Equation of straight line: Point slope formulam=y-y0x-x0
Equation of straight line: Point slope formulam=y-y0x-x0
Equation of straight line: two point formulay-y1x-x1=y2-y1x2-x1
Equation of straight line: slope intercept formy=mx+cwhere c is y-intercept
Equation of straight line: intercept formxa+yb=1where, a is x-intercept and b is y-intercept
Equation of straight line: normal formxcosπœ”+ysinπœ”=pwhere, p is normal distance of line from origin and πœ” is angle which normal makes with positive x-axis.
Conic Section
Axis: A line about which conic section is symmetric is called axis of conic section
Vertex: The point of intersection of conic section with its axis of symmetry is called vertex.
Focal distance: The distance of a point on a conic section from focus is called focal distance of a point.
Focal chord: A chord of a conic section passing through its focus is called a focal chord.
Pair of straight lines Theorem-1:Thejointequationofpairofstraightlinespassingthrutheoriginisahomogeneousequationofdegree2inxandyTheorem-2:Homogeneousequationofdegreetwoinxandy.i.eax2+2hxy+by2=0representsapairofstraightlinespassingthruoriginifh2-abβ©Ύ0ifh2-abβ©Ύ0thenthelinesarerealanddistinctifh2-ab=0thenthelinesarerealandcoincidentifh2-abβ©½0thentheslopeofthelinesarenotrealifm1andm2areslopeoflinesthenm1+m2=-2hbm1m2=abGeneralseconddegreeequationinxandyax2+2hxy+by2+2gx+2fy+c=0.Itrepresentspairofstraightlinesonlyif|ahghbfgfc|=0,i.e.abc+2fgh-af2-bg2-ch2=0pointofintersectionis:(hf-bgab-h2,gh-afab-h2)