Hi booper563,
The first line looks okay, but the second line isn't.Find the points of intersetion of the circle x^2+(y-1)^2=25 and y=-7x+26 by solving a system of equations.
So far I got
now what do I do am I doing it right?
Note that
Find the points of intersetion of the circle x^2+(y-1)^2=25 and y=-7x+26 by solving a system of equations.
So far I got x^2 +(-7x+26-1)^2=25
x^2+(7x^2)+26x-1=25
now what do I do am I doing it right?
B) Find the length of the chord determined by the poibnts of intersection in question a. Express your answer in simpliest radical form.
C) Determine the distance of the chord from the centre of the circle
Like i said before this math is REALLY confusing to me, so details and step by step instructions would be amazing help.
thanks guys
for the points of intersection you could use the method you used.
when both equations are combined you should get:
50x^2-350x+600=0
this factorises to: 50(x-4)(x-3)=0
hence x=4 and x=3 i.e. there are two points as you would expect (unless the circles are touching in which case there will be one).
Then substitute values of 3 and 4 into equations to get y and coordinates at each end.
The rest of the question should be relatively straight forward from here on.
Hello, booper563!
A) Find the points of intersection of the circle
We have: .
Simplify: .
Divide by 50: .
And we have: .
. . The intersections are: .
Use the Distance Formula on points andB) Find the length of the chord determined by the points of intersection in A.
. . Express your answer in simplest radical form.
. .
A handy fact: the radius to the midpoint of a chord is perpendicular to the chord.C) Determine the distance of the chord from the centre of the circle.
The midpoint of AB is: .
We want the distance from the center to
. .