Calculus & Analytic Geometry (B.A / B.Sc.)
Chapter:05 (Plane Curves I)
In this chapter, we will study the following topics:
- introduction
- curves in the cartesian plane
- properties of plane curves
- the straight line
- the slope-intercept form or the gradient form
- the normal form the equation
- the slope-one point form
- a straight line passing through two points
- equation of straight line passing through the intersection of two given straight lines
- the circle
- tangent to the circle
- real or imaginary tangent to a circle
- the conics equation
- the ellipse equation
- the hyperbola equation
- the eccentricity e of the ellipse
- the homogeneous equation
- the equation of the nth degree
- second-degree equation
- parametric representation
- parametric equation of the parabola
- the roulettes
- the cycloid
- hypocycloid
- the equation of hypocycloid
- equation of epicycloid
- the trochoid
- polar coordinates
- the cartesian equation of asteroid
- graphs of polar equation
- lemniscate
- relation between the polar and the cartesian coordinates
- tangents and normal
- cartesian coordinate
- parametric representation of cartesian coordinate coordinates
- tangent and normal to the parabola
- the geometrical significance
- parabolic reflector
- properties of the parabola
- the focus-directrix property
- the reflection property
- properties of the ellipse
- the focus-directrix property
- properties of the hyperbola
- polar equation of a conic
- pedal equation
- the pedal equation of cardioid
- change of axes
- translation of axes
- plot the equation
- extreme values of a function
- critical points
- concavity and convexity
- singular points
- cusp of the second kind
- find the asymptote
- curve tracing
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