Please help with 912 Write a conic equation in standard form

Please help with 9-12

Write a conic equation in standard form for each of the following descriptions (continued). 9. A circle centered 3 units below the origin with radius 4V3 10. A hyperbola with vertices at (l,6) and (1,-2) and asymptotes at y Ex+ and 4 10 11. 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. 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.

Solution

9. Centre of circle 3 units below origin i.e. ( 0 , -3)

radius = 4sqrt3

Std equation of circle : (x-h)^2 +(y-k)^2 = r^2

x^2 + ( y +3)^2 = 48