Math Problem Statement

Various geometry and algebra-related tasks, primarily involving circles, lines, and distances in Cartesian coordinates.

Solution

I see that you've uploaded a mathematical document in Slovak. I'll extract the contents and provide help with any of the questions you would like to solve or discuss. Here’s a translation of some of the questions:

  1. Task 9: Determine the equation of the lines gg and hh if their parametric equations are given as: g:t(42t,5t) for tR,h:t(2+s,1+3s) for sR.g: t \mapsto (4 - 2t, 5 - t) \text{ for } t \in \mathbb{R}, \quad h: t \mapsto (2 + s, 1 + 3s) \text{ for } s \in \mathbb{R}.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Analytic Geometry
Circles
Lines
Distance Formula
Parametric Equations

Formulas

Distance between two points: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Equation of a circle: (x - h)^2 + (y - k)^2 = r^2
General equation of a line: ax + by + c = 0

Theorems

Equation of a Circle Theorem
Distance Theorem
Slope-Intercept Form
Parametric Equations in Geometry

Suitable Grade Level

Grade 10-12