Option 7 IDS 4.1

IDZ - 4.1 No. 1.7. It is necessary to create canonical equations for the following curves: a) ellipse; b) hyperboles; c) parabolas. The following notation is used in the problem: A and B - points lying on the curve; F - focus; a - semimajor (real) axis; b - minor (imaginary) semi-axis; ε - eccentricity; y = ± kx - equations of hyperbola asymptotes; D - directrix of the curve; 2c - focal length. Given: a) a=4; F(3;0); b) b = 2√10; F(–11;0); c) D: x = –2.

No. 2.7. It is necessary to write down the equation of a circle passing through the indicated points and having a center at point A. Given: the foci of the ellipse 3x2 + 4y2 = 12; A is its top vertex.

No. 3.7. It is necessary to create an equation of a line, each point of which satisfies the given conditions. The line is located at a distance from point A(4;1) four times greater than from point B(–2;–1).

No. 4.7. It is necessary to construct a curve specified in the polar coordinate system: ρ = 2·(1 – cosφ).

No. 5.7. It is necessary to construct a curve defined by parametric equations (0 ≤ t ≤ 2π).

Option 7 IDS 4.1

This digital product contains solutions to problems from IPD 4.1 in mathematics. In it you will find the canonical equations for the ellipse, hyperbola and parabola, as well as the equation of the circle indicating the foci and the upper vertex of the ellipse. The product also contains the equation of a line that satisfies specified conditions, and curves specified in polar and parametric coordinate systems.

This product is suitable for both students who are preparing for math exams and teachers who are looking for materials to prepare for classes.

The beautiful design of the product's html code allows you to quickly and conveniently familiarize yourself with the contents and find the information you need.

Don't miss the opportunity to improve your math skills with this digital product!

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The product in this case is a mathematics task, which includes five tasks:

1. Compose the canonical equations of an ellipse, hyperbola and parabola, defined in various ways.

2. Find the equation of a circle with given foci and center.

3. Write an equation of a straight line, each point of which is at a certain distance from two given points.

4. Construct a curve specified in polar coordinates.

5. Construct a curve given by parametric equations.

All problems relate to various branches of mathematics and require knowledge of relevant theoretical information and the ability to apply them in practice.

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