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# Circle geometry watch

1. Here are some questions I sturggle with.

1.The line y=x+2 meets the curve x^2+4y^2-2x=35 at the point a and b find co ordinates of a and b.

What I did was input one equation into the other : x^2+4(x+2)(x+2)-2x=35 which equals 5x^2+14x-19 and the solutions to this is x=19/5 and x=1
the problem is that a and b do not pass through the x or y-axis.

2 (4 part question managed to do the first 2 parts)

(a) Find equation of line joining A(7,4) and B(2,0) gve answer in ax+by+c=0 format so 4x-5y-8=0

(b)Find length of AB in surd form

4-0=4 7-2=5
square root of 4^2+5^2 which is the root of 41.

(c)The point C has coordinate (2,t) where t>0 and AC=AB
find value of t

(d)Find area of triangle ABC

I cannot do c and b.
2. (Original post by Anonymous1502)
Here are some questions I sturggle with.

1.The line y=x+2 meets the curve x^2+4y^2-2x=35 at the point a and b find co ordinates of a and b.

What I did was input one equation into the other : x^2+4(x+2)(x+2)-2x=35 which equals 5x^2+14x-19 and the solutions to this is x=19/5 and x=1
the problem is that a and b do not pass through the x or y-axis.
I think your first x-coordinate should be -19/5, but otherwise this is fine. Why do you think that either point should lie on the axes (if this is what you are saying, I'm not quite sure how a point can pass though an axis)?
3. (Original post by Pangol)
I think your first x-coordinate should be -19/5, but otherwise this is fine. Why do you think that either point should lie on the axes (if this is what you are saying, I'm not quite sure how a point can pass though an axis)?
4. (Original post by Anonymous1502)
But A and B do clearly not lie on the axes. You need to find the y-coordinates that go with the x-coordinates you have found, and then the line that passes through both of these points will cut through the axes as shown in the diagram.
5. (Original post by Pangol)
But A and B do clearly not lie on the axes. You need to find the y-coordinates that go with the x-coordinates you have found, and then the line that passes through both of these points will cut through the axes as shown in the diagram.
How would you find the y cordinates?
6. (Original post by Anonymous1502)
How would you find the y cordinates?
You know that the points lie on the line y=x+2 and the curve x^2+4y^2-2x=35. Substitute the x-coordinates into one of these. One is considerably easier than the other!
7. (Original post by Pangol)
You know that the points lie on the line y=x+2 and the curve x^2+4y^2-2x=35. Substitute the x-coordinates into one of these. One is considerably easier than the other!
y=x+2 becomes y-2=x so (y-2)(y-2)+4y^2-2(y-2)=35
y^2-4y+4+4y^2-2y-4=35
5y^2-6y-35=0 which cannot be factorised.
8. (Original post by Anonymous1502)
y=x+2 becomes y-2=x so (y-2)(y-2)+4y^2-2(y-2)=35
y^2-4y+4+4y^2-2y-4=35
5y^2-6y-35=0 which cannot be factorised.
There is no need to do this. You know that y = x + 2. And you know the x-coordinates already. So you can easily find the y-coordinates.
9. (Original post by Pangol)
There is no need to do this. You know that y = x + 2. And you know the x-coordinates already. So you can easily find the y-coordinates.
y=1+2 y=-19/5+2
y=3 y=-9/5

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