Ryabushko A.P. IDZ 4.1 option 1

IDZ task - 4.1 No. 1.1. It is necessary to create a canonical equation for:

a) ellipse; b) hyperboles; c) parabolas;

where A and B are 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 - focal length.

Hopefully:

a) b = 15; F(–10;0); b) a = 13; ε = 14/13; c) D: x = –4.

No. 2.1. It is necessary to 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. 3.1. It is necessary to 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 as from point A(1;3).

No. 4.1. It is necessary to construct a curve specified in the polar coordinate system: ρ = 2·sin 4φ.

No. 5.1. It is necessary to construct a curve defined by parametric equations (0 ≤ t ≤ 2π).

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Welcome to our digital goods store! We are pleased to present you a unique product from the author Ryabushko A.P. - "IDZ 4.1 option 1".

This digital product is a detailed description of how to solve math problems. In this product you will find the canonical equations for the ellipse, hyperbola and parabola, as well as the equation of the circle and line, as well as curves defined in polar and parametric coordinate systems.

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Thank you for your purchase! If you have any questions or require assistance, please contact us at the email address listed on the Seller Information page.

This product is a detailed description of solving problems in mathematics within the framework of IPD 4.1 option 1, consisting of five tasks.

The first task requires you to create canonical equations for an ellipse, a hyperbola and a parabola. To do this, points A and B lying on the curve, focus F, semi-major axis a, semi-minor axis b, eccentricity ε, equations of the hyperbola asymptotes y = ± kx, directrix of the curve D and focal length 2c are given. For each curve a certain value of some parameters is given.

The second task requires writing the equation of a circle passing through the specified points and having a center at a given point A. For this, the coordinates of point A and the equation of a hyperbola specified in Cartesian coordinates are given.

The third task requires composing an equation of a line, each point of which is located from the straight line x = –6 at a distance twice as great as from the given point A(1;3).

The fourth task requires constructing a curve specified in the polar coordinate system: ρ = 2·sin 4φ.

The fifth task requires constructing a curve defined by parametric equations for values ​​of the parameter t in the range from 0 to 2π.

All information is presented in a beautiful HTML design, which makes the material easier to read and understand. If the buyer has questions or requires assistance, you can contact the seller at the email address indicated on the "seller information" page.

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Ryabushko A.P. IDZ 4.1 option 1 is an educational task that includes five problems of varying complexity from the field of mathematics. The assignment requires solving the following problems:

1. Compose canonical equations for the ellipse, hyperbola and parabola with the specified parameters (points, foci, semi-axes, eccentricities, etc.).
2. Write down the equation of a circle with a given center and passing through the indicated points.
3. Create an equation for a straight line that satisfies the given location conditions relative to the given points and the straight line.
4. Construct a curve specified in the polar coordinate system: ρ = 2·sin 4φ.
5. Construct a curve given by parametric equations.

These problems can be useful for learning mathematics and improving problem solving skills. If you have questions about solving problems, you can contact the seller listed in the seller information.

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