F.5 Maths equation of circle

2015-03-04 3:25 am

The line segment joining A(-5,2) and B(3,4) is a diameter of a circle. Find the
equation of the circle in the general form.

I have a few questions about the methods using by the book to do this question.
First method is finding out the centre and radius of the circle, then find the
equation of the circle. Second method is in the picture below:
http://postimg.org/image/lv9y9s9rx/

I have some questions about the second method. It is similar to a calculation as
below:
http://postimg.org/image/myu2lquf1/

In the second picture,the equation of locus is a circle excluding points A and B.
Then in the first picture, the book let point E be a point on the circle where
angle AEB=90 degree. But why in the calculation the book does not say that x is not equal to -5 and 2? Why we can use this method to find the equation of circle?
Please explain. Thank you~~

回答 (4)

happygay

2015-03-04 9:20 am

✔ 最佳答案

In the first place, please do INTERGRATE the maths concept and don't just memorize and recite the maths theorem (base angles, isos. triangles, etc.) and you cant get at least lv 5 in DSE gaa, I'm sure you want it, right??

1.
Q:Why in the calculation the book does not say that x is not equal to -5 and 2?
A:Actually if x is not equal to-5 or 2,angle AEB = 90 degree, so 2 expressions are actually the same. If x = -5 or 2, point E will lie on the diameter AB, which becomes point A or point B, thus ABE is collinear( in the same line) so the angle AEB will become 180 degrees.

2.
Q:Why we can use this method to find the equation of circle?
A:If AB is an diameter, a point in the circle, mark it as point E (except position of A &B) will make a right angle with A & B, you remember what's angle in semi-circle in Ch.10????so slope of AE times slope of BE =-1, since they are perpendicular, and then solve it using the coordinates of A,B and E (x,y)

dse仲有391日 lol
be fd ok? xppp
sorry for my goodest english lol

參考: myself

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