The Student Room Group

Circle geometry

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.
Reply 1
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)?
IMG_0559.jpg
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)?
Reply 3
Original post by Anonymous1502
IMG_0559.jpg


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.
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?
Reply 5
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!
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.
Reply 7
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.
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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