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Find the equation of the circle
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Could you help me solve this Problem I've been struggling with it.
The points A (1, 3), B (7, 1) and C (−3, −9) are joined to form a triangle.
It can be shown that ABC is right-angled with the right-angle at A.
The points A, B and C lie on the circumference of a circle.
Find the equation of the circle in the form Xsquared+ysquared+ax+by+c=0 (7marks)
The points A (1, 3), B (7, 1) and C (−3, −9) are joined to form a triangle.
It can be shown that ABC is right-angled with the right-angle at A.
The points A, B and C lie on the circumference of a circle.
Find the equation of the circle in the form Xsquared+ysquared+ax+by+c=0 (7marks)
Last edited by NATHANL123; 1 month ago
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#2
If the right angle is at A, then B and C are where the diameter touches the circle.
Because the midpoint of the diameter of the circle is the centre of the circle, if you just find the distance between B and C, you can find the midpoint,((x1+x2)/2, (y1+y2)/2).
Once you do that, tell me what you get
Because the midpoint of the diameter of the circle is the centre of the circle, if you just find the distance between B and C, you can find the midpoint,((x1+x2)/2, (y1+y2)/2).
Once you do that, tell me what you get
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(Original post by nm12345)
If the right angle is at A, then B and C are where the diameter touches the circle.
Because the midpoint of the diameter of the circle is the centre of the circle, if you just find the distance between B and C, you can find the midpoint,((x1+x2)/2, (y1+y2)/2).
Once you do that, tell me what you get
If the right angle is at A, then B and C are where the diameter touches the circle.
Because the midpoint of the diameter of the circle is the centre of the circle, if you just find the distance between B and C, you can find the midpoint,((x1+x2)/2, (y1+y2)/2).
Once you do that, tell me what you get
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(Original post by NATHANL123)
Would it be x^2+y^2-2x+4y-51=0?
Would it be x^2+y^2-2x+4y-51=0?
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#5
(Original post by NATHANL123)
Would it be x^2+y^2-2x+4y-51=0?
Would it be x^2+y^2-2x+4y-51=0?
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(Original post by mqb2766)
Do the points satisfy it? If not, there's a mistake.
Do the points satisfy it? If not, there's a mistake.
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#7
(Original post by NATHANL123)
I don't think so but i've just followed the method i've been taught but i keep getting the wrong answer
I don't think so but i've just followed the method i've been taught but i keep getting the wrong answer
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#8
(Original post by NATHANL123)
Would it be x^2+y^2-2x+4y-51=0?
Would it be x^2+y^2-2x+4y-51=0?
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#9
(Original post by NATHANL123)
And the centre of the circle is (2,-4)
And the centre of the circle is (2,-4)
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(Original post by mqb2766)
Pls don't upload answers.
Pls don't upload answers.
I wrote it all out again and I think I must have gotten confused when putting it into the first equation of a circle
Last edited by NATHANL123; 1 month ago
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#12
(Original post by NATHANL123)
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I wrote it all out again and I think I must have gotten confused when putting it into the first equation of a circle
I wrote it all out again and I think I must have gotten confused when putting it into the first equation of a circle
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