# SOLUTION: Hai Sir, please help me on this problem, i got stuck 2)The centre of a circle is (2x-1,7) and it passes through the point (-3,-1).If the diameter of the circle is 20units ,then

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 Click here to see ALL problems on Geometry Word Problems Question 398173: Hai Sir, please help me on this problem, i got stuck 2)The centre of a circle is (2x-1,7) and it passes through the point (-3,-1).If the diameter of the circle is 20units ,then find the values of x. Found 2 solutions by Edwin McCravy, lwsshak3:Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!Hai Sir, please help me on this problem, i got stuck 2)The centre of a circle is (2x-1,7) and it passes through the point (-3,-1).If the diameter of the circle is 20units ,then find the values of x. ``` The letter x is normally a variable, not an unknown constant. However the x in (2x-1,7) represents an unknown constant. So to avoid conflict of notation involving x as a variable and x as an unknown constant, I will change the x in the point to "a", which is a standard letter to use for an unknown constant. So let's pretend the problem was stated this way instead: ``` 2)The centre of a circle is (2a-1,7) and it passes through the point (-3,-1). If the diameter of the circle is 20 units, then find the values of a. ``` The equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r² So we substitute (h,k) = (2a-1,7), and since the diameter of the circle is 20 units, the radius is one-half that or r=10 (x - (2a-1))² + (y - 7)² = 10² Since we know that (-3,-1) is a point on the circle, we can substitute (x,y) = (-3,-1) (-3 - (2a-1) )² + (-1 - 7)² = 10² (-3 - 2a + 1)² + (-8)² = 100 (-2-2a)² + 64 = 100 (-2-2a)² = 36 -2 - 2a = ±√36 -2 - 2a = ±6 Using the + Using the - -2 - 2a = 6 -2 - 2a = -6 -2a = 8 -2a = -4 a = -4 a = 2 (x - (2a-1))² + (y - 7)² = 10² Using the + that becomes (x - (2(-4)-1))² + (y - 7)² = 10² (x - (-8-1))² + (y - 7)² = 10² (x - (-9))² + (y - 7)² = 10² (x + 9)² + (y - 7)² = 10² That's this red circle: ----------------------- (x - (2a-1))² + (y - 7)² = 10² Using the - that becomes (x - (2(2)-1))² + (y - 7)² = 10² (x - (4-1))² + (y - 7)² = 10² (x - (3))² + (y - 7)² = 10² (x - 3)² + (y - 7)² = 10² That's the green circle: Notice they both go through the point (-3,-1); in fact they intersect at that point and both have radius 10 and diameter 20. So the answers are a = -4 and a = 2. Edwin``` Answer by lwsshak3(6764)   (Show Source): You can put this solution on YOUR website!The centre of a circle is (2x-1,7) and it passes through the point (-3,-1).If the diameter of the circle is 20units ,then find the values of x. let us first start with the standard form for a circle. (x-h)^2+(y-k)^2=r^2 (h,k)= coordinates of the center r=radius of the circle given: diameter=20 or radius=10 y-coordinate of the center point on circle (-3,-1) let u=(2x-1),the x-coordinate of the center solving: (x-u)^2+(y-7)^2=10^2 (x-u)^2+(y-7)^2=100 x^2-2ux+u^2+y^2-14y+49=100 substitute (x,y) coordinates, (-3,-1) 9+6u+u^2+1+14+49=100 u^2+6u=100-73=27 u^2+6u-27=0 (u+9)(u-3)=0 u=-9 u=3 2x-1=u=-9 2x=-8 x=-4 2x-1=u=3 2x=4 x=2 ans: x=-4 x=2 These are two circles with different centers,(-9,7) and (3,7)