On a coordinate plane, a circle has a center at (negative 2, 1). which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0

The answer is: the first and the second are correct

Step-by-step explanation:

Data:

Center: (-2, 1)

a) x2 + y2 + 4x – 2y – 4 = 0

x2 + 4x       +y2 - 2y = 4

(x+2)2 + (y-1)2 = 4+4+1 = 9        Center = (-2,1)  Correct

b) x2 + y2 + 4x – 2y + 2 = 0

(x + 2)2 + (y-1)2 = -2+4+1 = 3      Center = (-2,1)  Correct

c) x2 + y² – 4x + 2y – 4 = 0

(x-2)2 + (y-1) = 4 + 4 +1 = 9         Center = (2,1)   Incorrect

d) x2 + y² – 4x + 2y + 2 = 0

(x-2)2 + (y -1)2 = -2+4+1 = 3      Center = (2,1)     Incorrect

Options A and B are correct.

Step-by-step explanation:

To get the correct answer we will convert each equation in the center radius form.

A). x² + y² + 4x - 2y - 4 = 0

x² + y² + 4x - 2y = 4

x² + 4x + 4 - 4 + y² - 2y + 1 - 1 = 4

(x + 2)²+ (y - 1)² - 5 = 4

(x + 2)²+ (y - 1)²= 9

Therefore, center of the circle is (-2, 1).

B). x² + y² + 4x - 2y + 2 = 0

x² + y² + 4x - 2y = -2

x² + 4x + 4 - 4 + y² - 2y + 1 - 1 = -2

(x + 2)² + (y - 1)² -5 = -2

(x + 2)² + (y - 1)²= -2+ 5

(x + 2)² + (y - 1)² = 3

Center of this circle is (-2, 1)

C). x² + y² - 4x + 2y - 4 = 0

(x² - 4x + 4 - 4) + (y² + 2y + 1 - 1) = 4

[(x - 2)² - 4]+ [(y + 1)²- 1] = 4

(x -2)² + (y + 1)² = 9

Center of this circle is (2, -1).

D). x² + y² - 4x + 2y + 2 = 0

x² - 4x + 4 - 4 + y² + 2y + 1 - 1 = -2

(x - 2)² - 4 + (y + 1)² - 1 = -2

(x -2)² + (y + 1)² - 5 = -2

(x -2)² + (y + 1)² = 3

Center of this circle is (2, -1)

Options A and B are correct.

im not sure

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.