Answer: Okay, the answer is x^2/68+(y+3)^2/17=1.
Step-by-step explanation: Step. 1 Complete the square for 4y^2+24y: 4(y+3)^2−36.
Step 2. You’ll need to substitute 4(y+3)^2−36 for 4y^2+24y in the equation x^2+4y^2+24y=32: x^2+4(y+3)^2–36=32.
Step 3. So you’ll need to move –36 to the right side of the equation by adding 36 to the both sides: x^2+4(y+3)^2=32+36.
Step 4 You add 32 and 36: x^2+4(y+3)^2=68.
Step 5. You divide each term by 68 to make the right side equal to one: x^2/68+4(y+3)^2/68=68/68.
And step 6. You’ll need to simplify each term in the equation in order to set the right side equal to 1. The standard form of an ellipse or hyperbola requires the right side of the equation be 1: x^2/68+(y+3)^2/17=1. I hope you download Math-way app to calculate this ellipse in standard form to be extremely helpful, please mark me as brainliest, and have a great weekend! :D
