Answer:
![(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}](https://tex.z-dn.net/?f=%28x%2B%20%5Cboxed%7B-5%7D%29%5E2%2B%28y%2B%5Cboxed4%29%5E2%3D%5Cboxed%7B100%7D)
Step-by-step explanation:
Given:
Center of circle is at (5, -4).
A point on the circle is ![(x_1,y_1)=(-3, 2)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%28-3%2C%202%29)
Equation of a circle with center
and radius 'r' is given as:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
Here, ![(h,k)=(5,-4)](https://tex.z-dn.net/?f=%28h%2Ck%29%3D%285%2C-4%29)
Radius of a circle is equal to the distance of point on the circle from the center of the circle and is given using the distance formula for square of the distance as:
Using distance formula for the points (5, -4) and (-3, 2), we get
![r^2=(5-(-3))^2+(-4-2)^2\\r^2=(5+3)^2+(-6)^2\\r^2=8^2+6^2\\r^2=64+36=100](https://tex.z-dn.net/?f=r%5E2%3D%285-%28-3%29%29%5E2%2B%28-4-2%29%5E2%5C%5Cr%5E2%3D%285%2B3%29%5E2%2B%28-6%29%5E2%5C%5Cr%5E2%3D8%5E2%2B6%5E2%5C%5Cr%5E2%3D64%2B36%3D100)
Therefore, the equation of the circle is:
![(x-5)^2+(y-(-4))^2=100\\(x-5)^2+(y+4)^2=100](https://tex.z-dn.net/?f=%28x-5%29%5E2%2B%28y-%28-4%29%29%5E2%3D100%5C%5C%28x-5%29%5E2%2B%28y%2B4%29%5E2%3D100)
Now, rewriting it in the form asked in the question, we get
![(x+ \boxed{-5})^2+(y+\boxed4)^2=\boxed{100}](https://tex.z-dn.net/?f=%28x%2B%20%5Cboxed%7B-5%7D%29%5E2%2B%28y%2B%5Cboxed4%29%5E2%3D%5Cboxed%7B100%7D)
Answer:
Rays: A, B, C, D - 4 rays for each.
Line segments: AB, BD, DC, CA.
Answer:
5x + 4y + 12 = 0
Step-by-step explanation:
Start with the point-slope equation of a straight line: y - k = m(x - h):
Here we are given the point (h, k): (-8, 7) and the slope m = -5/4. Inserting this info into the equation give above, we get: y - 7 = (-5/4)(x + 8).
We must put this equation into "standard form" Ax + By + C = 0.
Multiply all three terms by 4 to remove fractions: 4y - 28 = -5(x + 8), or
4y - 28 + 5x + 40 = 0
Rearranging these terms, we get 5x + 4y + 12 = 0, which is the desired equation in standard form.
F(x) = 3x^32 + 8x^2 -22x +43
The ends of all the polynomials with even degree behave like quadratic functions.
Given the the coefficient of x^32 is positive, the function opens upwards. Then the two ends go up.