Geometry

• Formulas for Area of a Triangle

1. , where is the base and is the altitude of the triangle. 2. Area of an equilateral triangle , where is the length of each side of the triangle. 3. Area of a triangle when two adjacent sides and the included angle is given by 4. Area of a triangle when length of all […]

• Formulas of Curvature and Radius of Curvature

The commonly used results and formulas of curvature and radius of curvature as shown below: 1. Curvature and radius of curvature for Cartesian curve is and 2. If the equation of the curve is given by the implicit relation , then and 3. If the curve is defined by parametric equations and then and so […]

• Equations of Asymptotes

Results and formulas related with Asymptotes are listed below: Asymptotes a.  Obtain by putting , in the highest degree terms of the equation of the curve. b.  Obtain by putting , in the degree terms of the equation of the curve. c. Obtain by putting , in the degree terms of the equation of the […]

• Formulas of Arc Length

Some important results and formulas regarding the Arc Length of the curve is listed here: 1.  Arc length for Cartesian curve is given by 2.  If the parametric form and is given, then 3.  The arc length if the equation of a curve in polar system i.e., is given by 4.  If the equation of […]

• Polar Equation of Conic

Some important results and formulas regarding the polar equation of conic are listed here: 1. Polar equation of conic is   If conic is an ellipse. If conic is hyperbola. If conic is parabola   2. Angle between two curve is given by   3. Two curves are perpendicular to each other if

• Equations of Tangent and Normal to a Hyperbola

Here we list the equation of tangent and normal for different forms of hyperbola: Equation of tangent to the hyperbola at is Equation of normal to the hyperbola at is Equation of tangent to the hyperbola at is Equation of normal to the hyperbola at is

• Equations of Tangent and Normal to a Ellipse

Here we list the equation of tangent and normal for different forms of ellipse also we define parallel chords and condition of tangency of an ellipse: Equation of tangent to the ellipse at is Equation of normal to the ellipse at is Equation of tangent to the ellipse at is Equation of normal to the […]

• Equations of Tangent and Normal to a Parabola

Here we list the equation of tangent and normal for different forms of parabola: Equation of tangent to the parabola at is Equation of normal to the parabola at is If then equation of normal line is The line touches the parabola if Equation of tangent to the parabola at is Equation of normal to […]

• Equations of Tangent and Normal to a Circle

Here we list the equation of tangent and normal for different forms of circle and also list the condition of tangency for the line to the circle: Equation of tangent to the circle at is Equation of normal to the circle at is Equation of tangent to the circle at is The condition of tangency […]

• Tangent and Normal Formulas

Formulas of Tangent and Normal to any curve at a given point are listed below: is the slope of the tangent to the curve at the point In a plane curve , Equation of the tangent at a point is Equation of the normal at a point is Consider that a curve is defined by […]

• Results and Formulas of Circle

01. Equation of the circles having the center at and radius is 02. Equation of the circle having the center and radius is 03.  Equation of the circle in general form is , whose centre is at and radius is 04. Equation of the circle passing through the point of intersection of the circles and […]

• Formulas and Results of Straight Lines

Consider two points and then 01. The distance formula 02. Midpoint formula 03. The point dividing in the ratio is 04. Slope of is 05. Slope of x-axis = zero 06. Slope of line parallel to x-axis = zero 07. Slope of y-axis is not defined i.e. 08. Slope of line parallel to y-axis is […]