Given end points of diameter,
(x1,y1)=(-3,-4)
(x2,y2)=(0,0)
Now,
the equation of circle is,
(x-x1)(x-x2)+(y-y1)(y-y2)=0
or, (x+3)(x-0)+(y+4)(y-0)=0
or, x^2 +3x +y^2 +4y =0
or, x^2 +y^2 +3x + 4y=0
which is in the form of x^2 +y^2 +2gx +2fy + c=0
where,
g=3/2
h=2
c=0
Now,
![radius(r) = \sqrt{ {g}^{2} + {f}^{2} - c } \\ = \sqrt{ \frac{ {3}^{2} }{ {2}^{2} } + {2}^{2} - 0 } \\ = \sqrt{ \frac{9}{4} + 4} \\ = \sqrt{ \frac{25}{4} } \\ = \frac{5}{2}](https://tex.z-dn.net/?f=radius%28r%29%20%3D%20%20%5Csqrt%7B%20%7Bg%7D%5E%7B2%7D%20%20%2B%20%20%7Bf%7D%5E%7B2%7D%20-%20c%20%20%7D%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B%20%7B3%7D%5E%7B2%7D%20%7D%7B%20%7B2%7D%5E%7B2%7D%20%7D%20%2B%20%20%7B2%7D%5E%7B2%7D%20%20-%200%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%5Cfrac%7B9%7D%7B4%7D%20%20%2B%204%7D%20%20%5C%5C%20%20%3D%20%20%20%5Csqrt%7B%20%5Cfrac%7B25%7D%7B4%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%7D%7B2%7D%20)
Answer:
Y=4,M=-1,X=2
4=-1(2)+b
4=-2+b
6=b
6
Step-by-step explanation:
Answer:
0.15 etc.
Step-by-step explanation:
Ok, so you want to substitute g and f in these equations so the f(x) = 2x+3x2-5 is equal to 10+6-5 or 11. The other equation is equal to 19. For the explanation put " I found this answer by substituting the given values for the variables in the equation". Your Welcome!
The formula of a distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
We have two points A(-5, 2) and B(-5, 8). Substitute:
![d=\sqrt{(8-2)^2+(-5-(-5))^2}=\sqrt{6^2+0^2}=\sqrt{6^2}=6](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%288-2%29%5E2%2B%28-5-%28-5%29%29%5E2%7D%3D%5Csqrt%7B6%5E2%2B0%5E2%7D%3D%5Csqrt%7B6%5E2%7D%3D6)
d is a diameter of a circle because d = 2r = 2(3).
The center of a circle is in midpoint of AB.
The formula of a midpoint:
![M\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)](https://tex.z-dn.net/?f=M%5Cleft%28%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5C%20%5Cdfrac%7By_1%2By_2%7D%7B2%7D%5Cright%29)
Substitute:
![\dfrac{-5+(-5)}{2}=\dfrac{-10}{2}=-5\\\\\dfrac{2+8}{2}=\dfrac{10}{2}=5](https://tex.z-dn.net/?f=%5Cdfrac%7B-5%2B%28-5%29%7D%7B2%7D%3D%5Cdfrac%7B-10%7D%7B2%7D%3D-5%5C%5C%5C%5C%5Cdfrac%7B2%2B8%7D%7B2%7D%3D%5Cdfrac%7B10%7D%7B2%7D%3D5)
Answer: (-5, 5).