Determine The General Form, C (-3,-2) Radius = 4, C (1,-2) Radius = 5/2 ? , -Step By Step Po, Please, Salamat Po

Determine the general form

c (-3,-2) radius = 4

c (1,-2) radius = 5/2 ?

-step by step po, please, salamat po

 

Answer:

General Form:

1) x² + y² + 6x + 4y - 3 = 0  

2) 4x² + 4y - 8x + 16y - 5 = 0

Step-by-step explanation:

The general form of equation of the circle is in expanded form:

x² + y² + Cx + Dy + F = 0

Where:

C, D, Y are constant

1)

Center (h,k): (-3,-2)

Radius: = 4

Write in Standard Form ⇒ (x - h)² + (y - k)² = r²:

(x - (-3))² + (y - (-2)² = (4)²

(x+3)² + (y+2)² = 16

Expand for the general form  x² + y² + Cx + Dy + F = 0:

(x+3)² + (y+2)² = 16

(x+3)(x+3) + (y+2)(y+2) - 16 = 0

x² + 6x + 9 + y² + 4y + 4 - 16 = 0

x² + y² + 6x + 4y + 9  + 4 - 16 = 0

x² + y² + 6x + 4y - 3 = 0   ⇒  General Form

2)

Center (h,k): (1, -2)

Radius = 5/2

Write in standard form (x - h)² + (y - k)² = r²:

(x - 1)² + (y - (-2))² = (5/2)²

(x - 1)² + (y + 2)² = 25/4

Expand for the general form x² + y² + Cx + Dy + F = 0:

(x - 1)² + (y + 2)² = 25/4

(x-1)(x-1) + (y+2)(y+2) -25/4 = 0

x² - 2x + 1 + y² +4y + 4 - 25/4 = 0

Multiply each term by the least common denominator (LCD) 4:

(4) x² - 2x + 1 + y² +4y + 4 - 25/4 = 0 (4)

4x² - 8x + 4 + 4y² + 16y + 16 - 25 = 0

4x² + 4y² - 8x + 16y + 4 + 16 - 25 = 0

4x² + 4y - 8x + 16y - 5 = 0 ⇒  General Form