Geometry
Problems related to shapes, spaces, measurements, etc.
Problems in this category
Given a right triangle $ABC$ with a right angle at $A$, and $\cos C = \frac{1}{3}$, find the values ...
TrigonometryRight TrianglesTrigonometric Identities
2025/6/1
A regular hexagon is inscribed in a circle with radius 10 cm. We need to find: 1. The length of one ...
HexagonCircleAreaPerimeterGeometric Shapes
2025/5/31
The problem asks us to eliminate the $xy$ term from the given equation $x^2 + xy + y^2 = 6$ by rotat...
Conic SectionsEllipseRotation of AxesCoordinate Geometry
2025/5/30
We are given several equations and asked to identify the conic or limiting form represented by each ...
Conic SectionsCirclesHyperbolasCompleting the Square
2025/5/30
The problem is to identify the type of conic section represented by each of the given equations. The...
Conic SectionsEllipseHyperbolaParabolaEquation of a Conic
2025/5/30
The problem asks for the $xy$-equation of a vertical ellipse centered at $(0, 0)$ with a major diame...
EllipseCoordinate GeometryEquation of an EllipseGeometric Shapes
2025/5/30
We are asked to identify the type of conic section represented by each given equation. The equations...
Conic SectionsEllipseHyperbolaParabolaEquation Analysis
2025/5/30
The problem asks us to identify the type of conic section represented by the given equation: $-\frac...
Conic SectionsParabolaHyperbolaEquation AnalysisCoordinate Geometry
2025/5/30
We are asked to find the standard equation of a parabola given its focus or directrix, assuming that...
ParabolaConic SectionsStandard Equation
2025/5/30
The problem asks us to find the coordinates of the focus and the equation of the directrix for each ...
Conic SectionsParabolasFocusDirectrixAnalytic Geometry
2025/5/30