IDZ Ryabushko 4.1 Option 1

No. 1 Compose the canonical equation: a) ellipse; b) hyperboles; c) parabolas; A; B - points lying on the curve; F - focus; a - semimajor (real) axis; b- minor (imaginary) semi-axis; ε - eccentricity; y = ± k x - equations of hyperbola asymptotes; D - directrix of the curve; 2c is the focal length. Given: a) b = 15; F( –10;0); b) a = 13; ε = 14 /13; c) D: x = – 4. No. 2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: A(0;–2); vertices of the hyperbola 12x2 – 13y2 = 156. No. 3 Create an equation of a line, each point M of which satisfies the given conditions. It is located at a distance twice as large from the straight line x = –6; than from point A(1;3). No. 4 Construct a curve specified in the polar coordinate system: ρ = 2·sin 4φ. No. 5 Construct a curve given by parametric equations ( 0 ≤ t ≤ 2π )

IDZ Ryabushko 4.1 Option 1 is a task with various mathematical problems, including composing equations of various curves and constructing their graphs in Cartesian and polar coordinate systems.

No. 1 - It is necessary to compose the canonical equations of the ellipse, hyperbola and parabola, knowing the coordinates of the focus, eccentricity, major and minor semi-axes, equations of the asymptotes of the hyperbola and the directrix of the curve. Each item contains one of these values.

No. 2 - It is required to write down the equation of a circle passing through given points and having a center at the specified point.

No. 3 - It is necessary to create an equation of a straight line, each point of which is located from a given straight line at a distance twice as great as from a given point.

No. 4 - It is necessary to construct a graph of a curve specified in the polar coordinate system.

No. 5 - It is required to construct a graph of a curve defined by parametric equations in a Cartesian coordinate system.

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