Circle Geometry with an Intersecting Line

[Physiona]

I'm requiring help on a circle geometry question I've done.
The line L, has equation of y=0, and intersects the circle with (3,0) and radius of 29. Find the points of intersection.
My working out:
29² = 841
It's centre is 3,0,
Inserting that in circle equation gives (x-3)²+y² = 841

Solving simultaneously,
(X-3)² + y² = 841 (1)
y=0 (2)
Sub (2) into (1)
(X-3)² + 0² = 841
x² -6x + 9 = 841
x²-6x+9-841=0
x²-6x-832=0
(X+26)(x-32)=0
X₁= -26 and x₂= 32

I'm stuck on what to do after this, I think I use process of elimination, however I'm not sure on the equation of y=0, as its confusing me with the zero and no other coefficients. Can someone help?
Thank you.

 

[FactChecker]

On the line y=0, x can have any value and y is always 0. So at the x values that you calculated, x=-26, and x=32, what y values would put it on the line?

PS. You might want to graph that line and the circle to see if there are easier ways to answer the problem.

 

[Physiona]

On the line y=0, x can have any value and y is always 0. So at the x values that you calculated, x=-26, and x=32, what y values would put it on the line?

PS. You might want to graph that line and the circle to see if there are easier ways to answer the problem.

Wouldn't the y values be 0, to put the x coordinates in the line? I have drawn the graphs, but I still don't get the correct answer.
The mark scheme says it intersects at (24,-20) and (-18,-20) I am not entirely sure where those values are from...

 

[Ray Vickson]

Wouldn't the y values be 0, to put the x coordinates in the line? I have drawn the graphs, but I still don't get the correct answer.
The mark scheme says it intersects at (24,-20) and (-18,-20) I am not entirely sure where those values are from...

Either the marking scheme is wrong or you have copied out the question incorrectly. On the line y=0 the intersection with the circle will always have second coordinate = 0.

 

[FactChecker]

Wouldn't the y values be 0, to put the x coordinates in the line?

Yes. You got the correct answer for the problem that you stated in the original post.

I have drawn the graphs, but I still don't get the correct answer.

If it made your calculated answers obvious, that was all that I was asking for. The graph should confirm your answers.

The mark scheme says it intersects at (24,-20) and (-18,-20) I am not entirely sure where those values are from...

That answer doesn't make sense.

 

[tnich]

The mark scheme says it intersects at (24,-20) and (-18,-20) I am not entirely sure where those values are from...

That would be the correct answer if the line were $y=-20$.

 

[Physiona]

Either the marking scheme is wrong or you have copied out the question incorrectly. On the line y=0 the intersection with the circle will always have second coordinate = 0.

If I'm honest, it's not an entire correct mark scheme instead it is a solution, so I think the solution itself is wrong, and is confusing me.

 

[Physiona]

That would be the correct answer if the line were $y=-20$.

Yes true, however the line is y=0, and the real agony is how I'm meant to actually get the points of intersection.

 

[Physiona]

Yes. You got the correct answer for the problem that you stated in the original post.If it made your calculated answers obvious, that was all that I was asking for. The graph should confirm your answers.That answer doesn't make sense.

Precisely. The solution is incorrect, and I'm not sure where to exactly progress on from there to get the right answer..

 

[FactChecker]

Precisely. The solution is incorrect, and I'm not sure where to exactly progress on from there to get the right answer..

Sorry, I was not clear. Your answer is correct for the line y=0 and the book answer is wrong . As @tnich stated, the book answer is correct for y=-20.

 

[Ray Vickson]

Precisely. The solution is incorrect, and I'm not sure where to exactly progress on from there to get the right answer..

What are you trying to say? I cannot understand the point you are making.

If the given answers are wrong there is nothing you can do to arrive at them in a correct way. Your answers to the stated problem are correct---end of story.

On the other hand, if the stated answer is correct your stated problem must be incorrect; there is no other possibility.

 

[Physiona]

Sorry, I was not clear. Your answer is correct for the line y=0 and the book answer is wrong . As @tnich stated, the book answer is correct for y=-20.
View attachment 221817

So my answer is correct. I'm just missing the y values though would they count as zero?

 

[Physiona]

What are you trying to say? I cannot understand the point you are making.

If the given answers are wrong there is nothing you can do to arrive at them in a correct way. Your answers to the stated problem are correct---end of story.

On the other hand, if the stated answer is correct your stated problem must be incorrect; there is no other possibility.

No you don't understand my point. I've worked out the x values, I'm missing the y values, due to the line equation of y=0.

 

[FactChecker]

So my answer is correct. I'm just missing the y values though would they count as zero?

Yes, the points in your answer are on the y=0 line. So (-26,0) and (32,0) are correct for the problem that you stated.

 

[CWatters]

If y=0 the problem seems rather too easy. It really looks like a typo and it should be y=-20.