We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
76
1
avatar

1. The equation of a circle is x^2 - 10x + y^2 + 8y - 8 = 0. What are the center and the radius of the circle? 

 

2. Write the equation of the cirlce in general form. 

3. Write the equation of a parabola shown in the picture. 

 Apr 23, 2019
 #1
avatar+5226 
+1

1) \(x^2 - 10x + y^2 + 8y -8 = 0\\ (x^2 - 10x +25 - 25)+ (y^2 +8y + 16-16)-8=0\\ (x-5)^2 - 25 + (y+4)^2-16 - 8 = 0\\ (x-5)^2+ (y+4)^2 = 49= 7^2\\ C=(5,-4),~r=7\)

 

2) \(\text{The center is at }(-2,3)\\ \text{The radius is }3\\ (x+2)^2 +(y-3)^2 = 9\)

 

3) \(\text{Vertex at }(2,3)\\ f(x) = a(x-2)^2+3\\ (0,4) \text{ on the parabola}\\ 4a+3=4\\ a=\dfrac 1 4\\ f(x) = \dfrac 1 4 (x-2)^2+3\)

.
 Apr 23, 2019

10 Online Users

avatar
avatar