Finding co-ordinates of a circle urgent help please!!!?

Point N Center ( 2, -1 ) , radius = 6.5

The chord AB of C is parallel to the x-axis, lies below the x-axis and is of length 12 units

as shown in Figure 3.

a) Find the coordinates of A and the coordinates of B.

The answer will be x1 = -4 and x2= 6

Y1 = y2 = -3.5

Please show your working!

Thank you so much!!

2 Answers

  • Jay V
    Lv 4
    9 years ago
    Favorite Answer

    Simply consider the triangle ABN. It is isosceles so AN = BN. We know this because AN and BN are radii of the same circle. Since AB || x axis, if we consider a point C in the midpoint of AB then CN is perpendicular to AB.

    AC = BC = 12/2 = 6

    AN = BN = 6.5

    therefore CN = (AN^2 - AC^2)^.5 = (42.25 - 36)^.5 = 6.25^.5 = 2.5cm by Pythagoras's theorem.

    Thus A - (2 - 6, -1 - 2.5) --> (-4, -3.5)

    B - (2 + 6, -1 -2.5) --> (8, -3.5)

    thus x2 is not 6 it is 8

  • chubb
    Lv 4
    3 years ago

    you may calculate ther co-ordinates of the centre as follows. First. although, in this variety of question that's a stable concept to making a drawing from the counsel you have been given. This normally enables you to work out the answer and would grant a verify on your calculations. So, on an (x,y)co-ordinate graph make A at factor x = a million, y = 3 and mark B at factor x = 7, y = -a million. Now connect A and B with a straight away line. when you consider that that's the diameter of the circle, the centre of the circle is the midpoint of this line and you will see that that's at approximately (4,a million). you may now see that undertaking will become one in each of looking the co-ordinates of the midpoint of a straight away line starting to be a member of things (x1,y1) and (x2,y2) using the formula: [x1 + x2]/2, [y1 - y2]/2 which for factors A and B provides: [a million + 7]/2, [3 + (-a million)]/2 =(4,a million) answer: the centre of the circle has co-ordinates (4,a million). word additionally that it is not correct which you %. as x1, y1 etc in basic terms be careful with indicators.

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