Write a conic equation in standard form for each of the following descriptions (

Question

Write a conic equation in standard form for each of the following descriptions (continued). A circle centered 3 units below the origin with radius 4 Squareroot 3 A hyperbola with vertices at (1, 6) and (1, -2) and asymptotes at y = 4/3 x + 2/3 y = = -4/3x + 10/3 A circle is defined as the set of all points (x, y) that lie a distance r from a point (h, k), which marks the center of the circle. a. Add points A, B, and C to the circle at the right such that A is the center, B is on the circle, and C is a point inside the circle such that AC BC. Give the coordinates of each point. A:____ B:_____ C:____ b. Use the Pythagorean Theorem to derive the equation for a circle with center (h, k) and radius r. Show each step of your derivation.

Explanation / Answer

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Given that circle is centered 3 units below origin.

=> Coordinates of center are (0,-3)

Equation of circle with center (h,k) and radius r is given by

(x-h)^2 + (y-k)^2 = r^2

(x-0)^2 + (y +3)^2 = (4sqrt(3))^2

x^2 + y^2 + 6y + 9 = 48

x^2 + y^2 + 6y + 39 = 0

Solution

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