Which is the standard form of the equation with p = 26, O= 3pi/4 ?
SQRT2x – SQRT2y = 0
SQRT2x – SQRT2y + 52 = 0
SQRT2x + 52 = 0
SQRT2x + 52y = 0
To determine the standard form of the equation with given values, we need to use the properties of trigonometric functions. In this case, we have p = 26 and O = 3π/4.
The standard form of the equation for a line is written as Ax + By + C = 0, where A, B, and C are coefficients.
To find these coefficients, we need to convert the given polar coordinates to Cartesian coordinates. This can be done using the following formulas:
x = p * cos(O)
y = p * sin(O)
Let's calculate these values step-by-step:
1. For x:
x = 26 * cos(3π/4)
= 26 * (-√2/2)
= -13√2
2. For y:
y = 26 * sin(3π/4)
= 26 * (√2/2)
= 13√2
Now, we substitute these values into the original equation SQRT2x – SQRT2y = 0:
SQRT2(-13√2) – SQRT2(13√2) = 0
-13 – 13 = 0
-26 = 0
Since -26 does not equal 0, the equation SQRT2x – SQRT2y = 0 is not satisfied.
Now, let's check the other options:
1. SQRT2x – SQRT2y + 52 = 0:
SQRT2(-13√2) – SQRT2(13√2) + 52 = 0
-13 – 13 + 52 = 0
26 + 52 = 0
78 = 0
Since 78 does not equal 0, the equation SQRT2x – SQRT2y + 52 = 0 is not satisfied.
2. SQRT2x + 52 = 0:
SQRT2(-13√2) + 52 = 0
-13 – 52 = 0
-65 = 0
Since -65 does not equal 0, the equation SQRT2x + 52 = 0 is not satisfied.
3. SQRT2x + 52y = 0:
SQRT2(-13√2) + 52(13√2) = 0
-13 + 52 = 0
39 = 0
Since 39 does not equal 0, the equation SQRT2x + 52y = 0 is not satisfied.
Based on these calculations, none of the provided equations satisfy the given values of p = 26 and O = 3π/4.
To determine the standard form of the equation, we need to simplify the given equation. Let's start by rearranging the terms:
SQRT2x - SQRT2y = 0
To eliminate the square roots, we need to perform the following steps:
Step 1: Move the SQRT2y term to the right-hand side:
SQRT2x = SQRT2y
Step 2: Square both sides of the equation to get rid of the square roots:
(SQRT2x)^2 = (SQRT2y)^2
2x = 2y
Now, the equation is simplified to:
2x - 2y = 0
This is the standard form of the equation. Therefore, the correct answer is:
SQRT2x - SQRT2y + 52 = 0