Standard form for both equation with steps
16x^2-96x+144+25y^2=400
16x^2+192x+576+25y^2=1600
To write the given equations in standard form, we need to rearrange the terms so that the variables are listed in alphabetical order, and the constant term is on the right side of the equation. Here are the steps to convert the equations:
Equation 1: 16x^2 - 96x + 144 + 25y^2 = 400
Step 1: Collect the constant terms on one side of the equation:
16x^2 - 96x + 25y^2 = 400 - 144
Simplifying, we get:
16x^2 - 96x + 25y^2 = 256
Equation 2: 16x^2 + 192x + 576 + 25y^2 = 1600
Step 1: Collect the constant terms on one side of the equation:
16x^2 + 192x + 25y^2 = 1600 - 576
Simplifying, we get:
16x^2 + 192x + 25y^2 = 1024
So, the standard form for Equation 1 is:
16x^2 - 96x + 25y^2 = 256
And the standard form for Equation 2 is:
16x^2 + 192x + 25y^2 = 1024