IDZ 4.1 – Option 25. Solutions Ryabushko A.P.

1. Drawing up canonical equations for various types of curves: a) ?ellipse: The equation of an ellipse in canonical form has the following form: (x - x0)^2/a^2 + (y - y0)^2/b^2 = 1, where ( x0, y0) - center coordinates

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IDZ 4.1 – Option 25. Solutions Ryabushko A.P.

This product is a solution to math problems designed in Microsoft Word 2003. The solution contains answers to the following tasks:

1. Compose canonical equations:

   a) ellipse; b) hyperboles; c) parabolas (A, B – points lying on the curve, F – focus, a – major (real) semi-axis, b – minor (imaginary) semi-axis, ε – eccentricity, y=±kx – equations of hyperbola asymptotes, D – directrix curve, 2c – focal length):

   а) a = 13, F(–5, 0); б) b = 4, F(–7, 0); в) D: x = –3/8.

2. Write down the equation of a circle passing through the indicated points and having a center at point A: 2.25.

3. Write an equation of a line, each point M of which satisfies the given conditions: 3.25.

   Distance from point A(5, 7) is four times greater than from point B(−2, 1).

4. Construct a curve given by an equation in a polar coordinate system: 4.25.

   ρ = 4(1 – sinφ).

5. Construct a curve given by parametric equations (0 ≤ t ≤ 2π): 5.25.

   x=3cos2t, y=3sin2t.

The solution uses a formula editor to visually demonstrate all mathematical calculations.

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