SOLUTION: Please help me with this!. A circle passes through the points (-3,1) and (-1,5). Its centre lies on the x-axis. Find (a) the coordinates of the centre, (b) the equation of the circ

Algebra ->  Length-and-distance -> SOLUTION: Please help me with this!. A circle passes through the points (-3,1) and (-1,5). Its centre lies on the x-axis. Find (a) the coordinates of the centre, (b) the equation of the circ      Log On


   

Question 989017: Please help me with this!. A circle passes through the points (-3,1) and (-1,5). Its centre lies on the x-axis. Find (a) the coordinates of the centre, (b) the equation of the circle and (c) if the point (1,p) also lies on this circle, find the possible values of p (leaving your answers in surd form if necessary).
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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(a)
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Standard form for circle:
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%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
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We know k=0, since center is on x axis. Using point (-3,1):
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%28-3-h%29%5E2%2B%281-0%29%5E2=r%5E2
9%2B6h%2Bh%5E2%2B1=r%5E2
h%5E2%2B6h%2B10=r%5E2
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Using point (-1,5)
%28-1-h%29%5E2%2B%285-0%29%5E2=r%5E2%0D%0A%7B%7B%7B1%2B2h%2Bh%5E2%2B25=r%5E2
h%5E2%2B2h%2B26=r%5E2
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Since both =r^2:
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h%5E2%2B6h%2B10=h%5E2%2B2h%2B26
4h-16=0
4h=16
h=4
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ANSWER (a): Co-ordinates of the center: (h,k)=(4,0)
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(b) Find the equation:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 (h,k)=(4,0)
%28x-4%29%5E2%2B%28y-0%29%5E2=r%5E2 Use point (-3,1) to find r^2
%28-3-4%29%5E2%2B%281-0%29%5E2=r%5E2
%28-7%29%5E2%2B%281%29%5E2=r%5E2
49%2B1=r%5E2
50=r%5E2
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ANSWER:(b): Equation of circle: %28x-4%29%5E2%2By%5E2=50
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(c) Point (1,p)
Using value (1)for x (p=y):
%281-4%29%5E2%2By%5E2=50
%28-3%29%5E2%2By%5E2=50
9%2By%5E2=50
y%5E2=41
y=(+ or -)sqrt%2841%29
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ANSWER: Possible values of p are (+ or -)sqrt%2841%29
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