Can someone please help me with this??Find the equation for the following parabola ( Parabolas) !

The equation of the parabola is (x - 2)² = 16(y + 1) ⇒ D

Step-by-step explanation:

The standard form of the equation of the parabola is

(x - h)²  = 4p(y - k), where

∵ The vertex of the parabola is (2, -1)

→ By using the notes above

∴ h = 2

∴ k = -1

∵ Its focus is (2, 3)

→ By comparing it with the notes above

∴ h = 2

∴ k + p = 3

∵ k = -1

→ Substitute it in the equation above

∴ -1 + p = 3

→ Add 1 to both sides

∵ -1 + 1 + p = 3 + 1

∴ p = 4

→ Substitute the value of h, k, p in the form of the equation above

∵ (x - 2)² = 4(4)(y - -1)

→ Remember (-)(-) = (+)

∴ (x - 2)² = 16(y + 1)

∴ The equation of the parabola is (x - 2)² = 16(y + 1)

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation:

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.