Lim En Jie's answer to Megan's Secondary 4 A Maths Singapore question.
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All normals to circle cut through the centre of circle. Using this we can sub 2 normal eqn together to find coordinates of centre. So left with radius which can find using (5,5). Thereafter just construct the equation.
Date Posted:
4 years ago
Megan, for such questions we need to find the centre of the circle, so we need some lines which pass through the centre of the circle.
These are represented usually by perpendicular bisectors of chords or the normal to the circle (which is technically the line perpendicular to the tangent to the circle at the point of tangency).
The reason for this has something to do with the symmetrical properties of a circle.
With two of such lines (which obviously have to be non-parallel) passing through the centre, their intersection HAS TO BE at the centre (two non-parallel lines intersect at only one point).
Once done, the centre of the circle is defined. The one other thing we need to define for a circle is its radius, which is found by connecting this centre to the point (5, 5) on the circle and calculating its length.
These are represented usually by perpendicular bisectors of chords or the normal to the circle (which is technically the line perpendicular to the tangent to the circle at the point of tangency).
The reason for this has something to do with the symmetrical properties of a circle.
With two of such lines (which obviously have to be non-parallel) passing through the centre, their intersection HAS TO BE at the centre (two non-parallel lines intersect at only one point).
Once done, the centre of the circle is defined. The one other thing we need to define for a circle is its radius, which is found by connecting this centre to the point (5, 5) on the circle and calculating its length.
thank you, now i understand:)
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