Writ the following equation in standard form. state wether the graph of the equation is a parabola, circle, ellipse or hyperbola.
x^2+4y^2+2x-24y+33=0

x² + 4y²+ 2x - 24y + 33 = 0

= (x+1)² + 4(y-3)² - 1 - 36 + 33 = 0

= (x+1)² + 4(y-3)² = 4

= (x + 1)²/2² + (y - 3)²/1² = 1

This is an Ellipse:  C(-1,3)

The Standard Form of an Equation of an Ellipse is : (x - h)²/a²/ (y - k)²/b² = 1

where Pt(h,k) is the center. (a variable positioned to correspond with major axis)

a and b  are the respective vertices distances from center

and√a² - b²are the foci distances from center: a > b

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)