In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis)
Answer:
The equation in standard form is ![(x + 1)^{2} + (y - 10)^{2} = 4](https://tex.z-dn.net/?f=%28x%20%2B%201%29%5E%7B2%7D%20%2B%20%28y%20-%2010%29%5E%7B2%7D%20%3D%204)
Step-by-step explanation:
The distance from (-1, 12) to (-1, 8) = 4 = diameter of the circle. So, 2 = radius
The center of the circle is at (-1, 10)
The equation in standard form is ![(x + 1)^{2} + (y - 10)^{2} = 4](https://tex.z-dn.net/?f=%28x%20%2B%201%29%5E%7B2%7D%20%2B%20%28y%20-%2010%29%5E%7B2%7D%20%3D%204)
100-27=73
Therefore you paid 73% of the original price. That’s the remaining percentage
Answer:
![x^2 + 4x + y^2 +8y = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%204x%20%2B%20y%5E2%20%2B8y%20%20%3D%20%200)
Step-by-step explanation:
Given
![A = (-1,-2)](https://tex.z-dn.net/?f=A%20%3D%20%28-1%2C-2%29)
![B = (2,4)](https://tex.z-dn.net/?f=B%20%3D%20%282%2C4%29)
![AP:BP = 1 : 2](https://tex.z-dn.net/?f=AP%3ABP%20%3D%201%20%3A%202)
Required
The locus of P
![AP:BP = 1 : 2](https://tex.z-dn.net/?f=AP%3ABP%20%3D%201%20%3A%202)
Express as fraction
![\frac{AP}{BP} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BAP%7D%7BBP%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
Cross multiply
![2AP = BP](https://tex.z-dn.net/?f=2AP%20%3D%20BP)
Calculate AP and BP using the following distance formula:
![d = \sqrt{(x - x_1)^2 + (y - y_1)^2}](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x%20-%20x_1%29%5E2%20%2B%20%28y%20-%20y_1%29%5E2%7D)
So, we have:
![2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}](https://tex.z-dn.net/?f=2%20%2A%20%5Csqrt%7B%28x%20-%20-1%29%5E2%20%2B%20%28y%20-%20-2%29%5E2%7D%20%3D%20%5Csqrt%7B%28x%20-%202%29%5E2%20%2B%20%28y%20-%204%29%5E2%7D)
![2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}](https://tex.z-dn.net/?f=2%20%2A%20%5Csqrt%7B%28x%20%2B1%29%5E2%20%2B%20%28y%20%2B2%29%5E2%7D%20%3D%20%5Csqrt%7B%28x%20-%202%29%5E2%20%2B%20%28y%20-%204%29%5E2%7D)
Take square of both sides
![4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2](https://tex.z-dn.net/?f=4%20%2A%20%5B%28x%20%2B1%29%5E2%20%2B%20%28y%20%2B2%29%5E2%5D%20%3D%20%28x%20-%202%29%5E2%20%2B%20%28y%20-%204%29%5E2)
Evaluate all squares
![4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16](https://tex.z-dn.net/?f=4%20%2A%20%5Bx%5E2%20%2B%202x%20%2B%201%20%2B%20y%5E2%20%2B4y%20%2B%204%5D%20%3D%20x%5E2%20-%204x%20%2B%204%20%2B%20y%5E2%20-%208y%20%2B%2016)
Collect and evaluate like terms
![4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20](https://tex.z-dn.net/?f=4%20%2A%20%5Bx%5E2%20%2B%202x%20%2B%20y%5E2%20%2B4y%20%2B%205%5D%20%3D%20x%5E2%20-%204x%20%2B%20y%5E2%20-%208y%20%2B%2020)
Open brackets
![4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20](https://tex.z-dn.net/?f=4x%5E2%20%2B%208x%20%2B%204y%5E2%20%2B16y%20%2B%2020%20%3D%20x%5E2%20-%204x%20%2B%20y%5E2%20-%208y%20%2B%2020)
Collect like terms
![4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0](https://tex.z-dn.net/?f=4x%5E2%20-%20x%5E2%20%2B%208x%20%2B%204x%20%2B%204y%5E2%20-y%5E2%20%2B16y%20%2B%208y%20%20%2B%2020%20-%2020%20%3D%20%200)
![3x^2 + 12x + 3y^2 +24y = 0](https://tex.z-dn.net/?f=3x%5E2%20%2B%2012x%20%2B%203y%5E2%20%2B24y%20%20%3D%20%200)
Divide through by 3
![x^2 + 4x + y^2 +8y = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%204x%20%2B%20y%5E2%20%2B8y%20%20%3D%20%200)
Step-by-step explanation:
Numbers: 330, 440, 550, 660 and so on all the way to 990