Standard form for both equation with steps
16x^2-96x+144+25y^2=400
16x^2+192x+576+25y^2=1600
These are the same kind. I'll do one.
Do them by completing the square:
16x^2-96x+144+25y^2=400
16(x^2-6x+9) + 25y^2 = 400
16(x-3)^2 + 25y^2 = 400
Now divide by 400 and you have
(x-3)^2/25 + y^2/16 = 1
To write both equations in standard form, you need to rearrange the terms so that the variables are listed in alphabetical order and the constant term is on the other side of the equation. Here are the steps for both equations:
Equation 1: 16x^2 - 96x + 144 + 25y^2 = 400
Step 1: Combine the constant terms on one side of the equation:
16x^2 - 96x + 25y^2 = 400 - 144
Step 2: Simplify the equation:
16x^2 - 96x + 25y^2 = 256
Equation 2: 16x^2 + 192x + 576 + 25y^2 = 1600
Step 1: Combine the constant terms on one side of the equation:
16x^2 + 192x + 25y^2 = 1600 - 576
Step 2: Simplify the equation:
16x^2 + 192x + 25y^2 = 1024
Now, both equations are in standard form. Equation 1 is: 16x^2 - 96x + 25y^2 = 256, and Equation 2 is: 16x^2 + 192x + 25y^2 = 1024.