Answer:
The equation of the ellipse in standard form is 4x²/361 + y²/36 = 1
Step-by-step explanation:
* Lets revise the equation of the ellipse
- The standard form of the equation of an ellipse with center (0 , 0 )
and major axis parallel to the x-axis is x²/a² + y²/b² = 1
# a > b
- The length of the major axis is 2a
- The coordinates of the vertices are ( ± a , 0 )
- The length of the minor axis is 2b
- The coordinates of the co-vertices are ( 0 , ± b )
- The coordinates of the foci are ( ± c , 0 ) , where c ² = a ² − b²
* Lets solve the problem
∵ The center of the ellipse is (0 ,0)
∵ Its width is 19 units
∴ The length of the major axis is = 19
∴ 2a = 19 ⇒ divide both sides by 2
∴ a = 19/2 ⇒ ∴ a² = 361/4
∵ Its height is 12 units
∴ The length of the minor axis is = 12
∴ 2b = 12 ⇒ divide both sides by 2
∴ b = 12/2 = 6 ⇒ ∴ b² = 36
- Lets write the equation in standard form
∵ The equation is x²/a² + y²/b² = 1
∴ x²/(361/4) + y²/36 = 1 ⇒ simplify it
∴ 4x²/361 + y²/36 = 1
* The equation of the ellipse in standard form is 4x²/361 + y²/36 = 1
and 
. The midpoint would then be
.
