Parabola

Formulas are organized based on their importance in the CAT exam.
1 Standard Equation of a Parabola
2 Condition for a Line to Cut the Parabola at Two Points
3 Chord of Contact (Parabola)
4 Pair of Tangents from a Point
5 Eccentricity Definition (Parabola)
6 Chord with Given Midpoint
7 Normal Perpendicular to a Given Line
8 Parabola Opening Towards Positive $$y$$-Axis
9 Focus of a Vertically Shifted Parabola
10 Tangent Length from Vertex
11 Intersection of Tangents at Parameters $$t_1,t_2$$
12 General Parabola with Vertex $$(h,k)$$
13 Eccentricity of a Parabola
14 Condition for a Line to Be Tangent
15 Directrix of a Shifted Parabola
16 Parametric Coordinates for a Shifted Vertical Parabola
17 Standard Equation of a Parabola
18 Equation of a Tangent Using Point of Contact
19 Area of Segment of a Parabola
20 Focus-Directrix Definition
21 Axis of $$x^2=4ay$$
22 Length of Tangent from an External Point
23 Intersection of a Tangent and a Normal
24 Tangent Perpendicular to a Given Line
25 Equation of Normal Using Point of Contact
26 Length of Focal Chord
27 Focal Distance in Cartesian Coordinates
28 Endpoints of the Latus Rectum
29 Parabola Opening Towards Positive $$y$$-Direction
30 Parabola Opening Towards Negative $$y$$-Axis
31 Condition for Two Tangents to Be Real
32 Tangent Chord Intersection
33 Subtangent
34 Area of Triangle Formed by Two Parametric Points and the Focus
35 Parabola Opening Towards Negative $$x$$-Axis
36 Tangent at a Point $$(x_1,y_1)$$
37 Axis of a Shifted Parabola
38 Parabola Opening Towards Negative $$y$$-Direction
39 Vertex of a Vertically Shifted Parabola
40 Condition for a Line to Be a Normal
41 Directrix of $$y^2=4ax$$
42 Tangent to a Shifted Vertical Parabola
43 Length of Latus Rectum for Shifted Parabola
44 Normal to a Shifted Vertical Parabola
45 Intersection of Tangents for a Shifted Horizontal Parabola
46 Focal Distance of a Parametric Point
47 Chord of a Parabola with Given Slope
48 Parabola Opening Towards Negative $$x$$-Direction
49 Normal Parallel to a Given Line
50 Condition for a Chord to Pass Through a Fixed Point
51 Slope of Normal at Parameter $$t$$
52 Condition for a Line to Be Tangent
53 Axis of $$y^2=4ax$$
54 Chord Length Cut by a Line
55 Condition for a Point to Lie Inside or Outside a Parabola
56 Normal in Parameter Form
57 Directrix of a Vertically Shifted Parabola
58 Distance of a Parametric Point from the Directrix
59 Number of Normals from a Point
60 Length of the Focal Radius
61 Vertex of $$y^2=4ax$$
62 Latus Rectum as a Focal Chord
63 Area of Triangle Formed by Focus and Latus Rectum
64 Length of Latus Rectum
65 Normal to a Shifted Horizontal Parabola
66 Point of Contact of a Tangent with Slope $$m$$
67 Focal Property
68 Tangent Parallel to a Given Line
69 Tangent in Slope Form
70 Tangents at the Ends of a Focal Chord
71 Normal at a Point $$(x_1,y_1)$$
72 Equation of Tangent in Normal Form
73 Parametric Coordinates for a Shifted Horizontal Parabola
74 Equation of a Focal Chord
75 Equation from Focus and Directrix
76 Point of Contact of a Normal
77 Normal at a Point in Parametric Form
78 Midpoint of a Chord
79 Focus of $$y^2=4ax$$
80 Area of the Triangle Formed by Tangent, Axis and Ordinate
81 Chord Joining Two Parameters of a Shifted Horizontal Parabola
82 Distance from a Point on the Parabola to the Directrix
83 Tangents at Two Parametric Points
84 Area Under a Parabola
85 Distance Between Two Parametric Points
86 Area Between a Parabola and Its Chord
87 Focus of a Shifted Parabola
88 Diameter Corresponding to Chord Slope
89 Condition for a Point to Be on the Directrix
90 Parametric Coordinates of $$x^2=4ay$$
91 Focal Chord
92 Area of Triangle Formed by Two Tangents and Their Chord of Contact
93 Product of Parameters of Normals
94 Condition for a Chord to Pass Through the Vertex
95 Normal at Parameter $$t$$ in Parametric Coordinates
96 Tangent and Chord Angle Property
97 Focal Distance of a Point
98 Chord of Contact from an External Point
99 Intersection of Tangents at the Ends of a Focal Chord
100 Normal at Parameter $$t$$
101 Condition for a Line to Intersect a Parabola
102 Tangent at Parameter $$t$$
103 Sum of Parameters of Normals
104 Product of Perpendicular Distances from a Point on the Parabola
105 Distance from Vertex to a Parametric Point
106 Axis of a Vertically Shifted Parabola
107 Intersection of Two Normals
108 Parabola as a Locus of Equal Distances
109 Reflection Property of a Parabola
110 Normal to Parabola
111 Tangent to a Shifted Horizontal Parabola
112 Parametric Coordinates of $$y^2=4ax$$
113 Latus Rectum of a Shifted Parabola
114 Focal Property in Cartesian Form
115 Tangent at the Latus Rectum Endpoints
116 Tangent at Parameter $$t$$ in Parametric Coordinates
117 Subnormal
118 Normal at the Vertex
119 Locus of Midpoints of Parallel Chords
120 Tangent at Vertex
121 Endpoints of Latus Rectum for a Shifted Parabola
122 Normal as the Angle Bisector
123 Parametric Equation (Parabola)
124 Equation of Chord of Contact in Parameter Form
125 Tangent at a Point in Parametric Form
126 Chord with a Given Slope
127 Chord Length in Terms of Parameters
128 Diameter Corresponding to a Family of Parallel Chords
129 Condition for a Chord to Pass Through the Focus
130 Pair of Tangents from an External Point
131 Diameter of a Parabola
132 Vertex of a Shifted Parabola
133 Equation of Chord Joining Parameters $$t_1,t_2$$
134 Slope of Tangent at Parameter $$t$$
135 Tangent at the Vertex
136 Chord of Contact from a Point $$(x_1,y_1)$$