Ellipse

Formulas are organized based on their importance in the CAT exam.
1 Relation Between Focal Distance and Eccentricity
2 Maximum Distance of a Tangent from the Centre
3 Normal at a Parametric Point of a Translated Ellipse
4 Area Ratio with the Circumscribed Rectangle
5 Condition for a Line to Lie Outside the Ellipse
6 Focus-Directrix Property
7 Minimum Length of a Focal Chord
8 Angle Between Two Tangents
9 Tangent Length from a Point on the Minor Axis
10 Length of Latus Rectum
11 Area of Ellipse
12 Distance of a Point from the Centre in Parametric Form
13 Director Circle (Ellipse)
14 Semi-Latus Rectum in Terms of Eccentricity
15 Tangent Parallel to a Given Line
16 Focal Property of a Translated Ellipse
17 Equation of the Latus Rectum
18 Condition for a Point to Lie Outside the Ellipse
19 Distance Between Parallel Tangents
20 Standard Equation with Vertical Major Axis
21 Relation Between Slopes of Conjugate Diameters
22 Endpoints of the Conjugate Diameter
23 Foci of a Translated Horizontal Ellipse
24 Minimum Distance of a Point from the Centre
25 Parametric Coordinates of a Translated Ellipse
26 Pair of Parallel Tangents
27 Condition for a Line to Cut the Ellipse
28 Length of a Chord with Given Distance from Centre
29 Equation of a Diameter with Given Slope
30 Tangents at the Minor-Axis Vertices
31 Eccentricity from the Focal and Major Axes
32 Ratio of Ellipse Area to Vertex Quadrilateral Area
33 Eccentricity from the Axes
34 Focal Distance of a Parametric Point
35 Product of Focal Distances in Cartesian Form
36 Chord of Contact from an External Point
37 Equation of a Diameter
38 Relation Between Semi-Axes and Focal Distance
39 Polar of a Point on the Minor Axis
40 Length of Diameter with Given Slope
41 Endpoints of the Other Latus Rectum
42 Maximum Area of the Triangle Formed by Two Foci and a Point
43 Diameter Corresponding to a Chord of Given Slope
44 Parametric Coordinates
45 Normal in Slope Form
46 Maximum Distance of a Point from the Centre
47 Area of Triangle Formed by Two Foci and a Point on the Ellipse
48 Foci of a Translated Vertical Ellipse
49 Minimum Diameter
50 Pair of Tangents from a Point on the Major Axis
51 Equation of Chord Joining Two Parametric Points
52 Equation of a Chord in General Form
53 Condition for a Line to Intersect the Ellipse
54 Relation Between Semi-Axes and Latus Rectum
55 Length of a Focal Chord
56 Relation Between Focal Separation and Axes
57 Eccentricity of an Ellipse
58 Endpoints of a Diameter
59 Tangent Length from a Point on the Major Axis
60 Length of Minor Axis
61 Focal Distances in Parametric Form
62 Reflection Property of an Ellipse
63 Equation of a Normal in Parametric Form
64 Product of Focal Distances
65 Equation of a Focal Chord Through a Focus
66 Focal Property of an Ellipse
67 Self-Pole Condition
68 Difference of Focal Distances in Parametric Form
69 Tangent at a Parametric Point
70 Condition for a Normal to Pass Through a Given Point
71 Individual Focal Distances in Parametric Form
72 Pair of Tangents from an External Point
73 Area of the Triangle Formed by Two Conjugate Semi-Diameters
74 Condition for a Point to Lie on the Ellipse
75 Condition for a Chord to Pass Through the Centre
76 Condition for a Line to Be a Secant
77 Chord Joining Two Parametric Points
78 Condition for Two Real Tangents
79 Slope of a Diameter
80 Tangent Condition in General Line Form
81 Length of Tangent from an External Point
82 Conjugate Diameter Relation
83 Distance from Centre to a Tangent
84 Director Circle
85 Condition for Two Tangents to Be Perpendicular
86 Maximum Length of a Focal Chord
87 Length of a Horizontal Chord
88 Focal Chord
89 Minimum Length of a Diameter
90 Equation of a Translated Ellipse
91 Equation of a Translated Vertical Ellipse
92 Relation Between Major Axis, Minor Axis and Eccentricity
93 Co-vertices of a Translated Vertical Ellipse
94 Area of Triangle Formed by a Point and the Centre
95 Tangent to a Translated Ellipse
96 Minimum Distance Between Parallel Tangents
97 Normal at a Parametric Point
98 Eccentric Angle
99 Sum of Focal Distances in Parametric Form
100 Slope of Tangent at a Parametric Point
101 Semi-Minor Axis in Terms of Eccentricity
102 Area of Parallelogram Formed by Conjugate Diameters
103 Normal in Terms of Eccentric Angle
104 Condition for a Point to Lie Inside the Ellipse
105 Condition for a Line to Touch the Ellipse
106 Director Circle of an Ellipse
107 Equation of a Chord with Given Slope
108 Length of Intercept Made by a Line Through the Centre
109 Tangent at a Point
110 Maximum Diameter
111 Tangent in Slope Form
112 Relation Between the Major and Minor Axes
113 Maximum Length of a Chord
114 Chord with Given Midpoint
115 Relation Between Latus Rectum and Eccentricity
116 Focal Chord Through a Focus in Polar Form
117 Standard Equation of an Ellipse
118 Length of a Diameter in a Given Direction
119 Distance Between the Directrices
120 Co-vertices of a Translated Horizontal Ellipse
121 Length of a Semi-Diameter in a Given Direction
122 Focal Distance at the Co-Vertex
123 Chord of Contact from a Point on the Major Axis
124 Normal to a Translated Ellipse
125 Midpoint of a Chord
126 Pair of Tangents from a Point on the Minor Axis
127 Eccentricity in Terms of the Semi-Axes
128 Normal at the Minor-Axis Vertices
129 Chord Perpendicular to the Minor Axis
130 Endpoints of the Latus Rectum
131 Length of Major Axis
132 Normal at a Point
133 Equation of the Diameter Through the Centre
134 Conjugate Diameters
135 Directrices of a Horizontal Ellipse
136 Directrix of a Translated Horizontal Ellipse
137 Tangent Perpendicular to a Given Line
138 Area of the Quadrilateral Formed by the Foci and Vertices
139 Relation Between Eccentric Angle and Slope of Chord
140 Circumference Approximation of an Ellipse
141 Condition for a Line to Lie Outside the Ellipse
142 Foci of a Horizontal Ellipse
143 Focal Chord Through the Other Focus
144 Distance Between the Vertices
145 Polar of a Point
146 Tangent in Terms of Eccentric Angle
147 Polar of a Point on the Major Axis
148 Foci of a Vertical Ellipse
149 Semi-Latus Rectum
150 Slope of Normal at a Parametric Point
151 Distance Between Two Parametric Points
152 Vertices of a Translated Horizontal Ellipse
153 Sum and Difference of Focal Distances
154 Eccentricity Definition (Ellipse)
155 Parametric Equation (Ellipse)
156 Equation of a Chord with Midpoint
157 Vertices of a Translated Vertical Ellipse
158 Chord of Contact (Ellipse)
159 Area of the Quadrilateral Formed by the Vertices
160 Distance Between the Co-vertices
161 Distance of a Chord from the Centre
162 Distance Between the Foci
163 Pole of a Line
164 Area of the Parallelogram Formed by Conjugate Diameters
165 \Relation Between Semi-Latus Rectum and Eccentricity
166 Normal to Ellipse
167 Area of the Ellipse
168 Equation of the Other Latus Rectum
169 Sum of Focal Distances
170 Directrices of a Vertical Ellipse
171 Relation Between Eccentricity and Focal Distance
172 Equation of a Normal at a Vertex
173 Maximum Distance Between Parallel Tangents
174 Focal Distance at the Major-Axis Vertex
175 Condition for a Line to Be Tangent
176 Diameter of an Ellipse
177 Chord Parallel to a Given Line
178 Angle Between Conjugate Diameters
179 Endpoints of a Pair of Conjugate Diameters
180 Sum of Reciprocal Focal Distances
181 Product of Focal Distances
182 Tangent at a Parametric Point of a Translated Ellipse
183 Distance Between Diametrically Opposite Points
184 Normal as the Angle Bisector
185 Co-vertices of a Horizontal Ellipse
186 Latus Rectum in Terms of Eccentricity
187 Chord Through a Given Point
188 Length of a Vertical Chord
189 Chord of Contact from a Point on the Minor Axis
190 Tangent as the External Angle Bisector
191 Tangents at the Major-Axis Vertices
192 Focal Distance in Terms of Eccentricity
193 Distance Between the Foci and a Vertex
194 Distance Between the Foci and a Co-vertex
195 Condition for Two Tangents to Be Perpendicular
196 Chord of Contact as Polar
197 Vertices of a Horizontal Ellipse
198 Area of Triangle Formed by the Two Foci and a Major-Axis Vertex