IDZ Ryabushko 4.1 Variant 1
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№1 Make a canonical equation: a) an ellipse; b) hyperbole; c) parabolas; A; In - points lying on the curve; F is the focus;
a - major (actual) axis; b - small (imaginary) axis; ε is the eccentricity; y = ± k x are the equations of the asymptotes of the hyperbola; D is the director 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.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: A (0; –2); the vertices of the hyperbole are 12x2 - 13y2 = 156.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line x = –6 at a distance twice as large; than from point A (1; 3).
№4 Construct a curve defined in the polar coordinate system: ρ = 2 · sin 4φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
a - major (actual) axis; b - small (imaginary) axis; ε is the eccentricity; y = ± k x are the equations of the asymptotes of the hyperbola; D is the director 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.
№2 Write down the equation of a circle passing through the indicated points and having a center at point A. Given: A (0; –2); the vertices of the hyperbole are 12x2 - 13y2 = 156.
№3 Draw up the equation of the line, each point M of which satisfies the given conditions. It is spaced from the line x = –6 at a distance twice as large; than from point A (1; 3).
№4 Construct a curve defined in the polar coordinate system: ρ = 2 · sin 4φ.
№5 Construct a curve given by parametric equations (0 ≤ t ≤ 2π)
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