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Need help with C1 Question

How would you work out the answer to this question:

The Straight line y=20-3x meets the circle x^2+y^2-2x-14y=0 at the points A and B. Calculate the exact length of the chord AB.


I understand this is probably an easy question but I am a weak candidate. Thanks in advance.
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Avatar for Gemini92
Gemini92
Original post by naz_ox
How would you work out the answer to this question:

The Straight line y=20-3x meets the circle x^2+y^2-2x-14y=0 at the points A and B. Calculate the exact length of the chord AB.


I understand this is probably an easy question but I am a weak candidate. Thanks in advance.


First work out the two sets of coordinates where the line and the circle intersect and then work out the distance between them using pythagorus.
Reply 2
Avatar for naz_ox
naz_ox
OP
2
Original post by Gemini92
First work out the two sets of coordinates where the line and the circle intersect and then work out the distance between them using pythagorus.


sorry I don't get it when you say work out the coordinates, of what?
Original post by naz_ox
sorry I don't get it when you say work out the coordinates, of what?


Work out the co-ordinates of the points of intersection of the line and circle. You have a pair of simultaneous equations which you can solve by substitution. The distance between these points is obviously the length of the chord.
Original post by naz_ox
sorry I don't get it when you say work out the coordinates, of what?


If you plotted the straight line and the circle using the equation given, they would intersect at two points (A and B). On a graph, these points will have x,y coordinates.

Can you see that?
Reply 5
Avatar for Gemini92
Gemini92
Original post by naz_ox
sorry I don't get it when you say work out the coordinates, of what?


The line and the circle intersect at two points which each have a set of coordinates. You need to work these out by replacing y in the circle equation with 20-3x (taken from the equation of the line). Solve the equation to obtain the two values of x and work out the corresponding values of y by using the line equation on each x value.
Original post by vruti123
x


Please post this somewhere more suitable.

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