Mathematics for PAT Question Help

This question is meant to be very straightforward but yet I am struggling with it. Someone pls help!!!

Q) A circle has radius of 5 units and its centre lies at (k,k+1) where k is a positive integer. Given that the co ordinate axes are tangents to the circle. Find the equation of the line which joins the two points where the circle intersects the co-ordinate axes. (3)

Answer is meant to be y= -4/3x + 4

Reply 1

tonyiptony

11

What are you struggling with? How much progress did you make?

Assuming you've not written down anything, a good diagram is a good start.

EDIT: I think I've jumped the gun again. The problem doesn't make sense to me. If the x- and y-axes are tangents of a circle, the center of the circle must be (k,k) or (k,-k), which is impossible here. Or unless I've misunderstood the question...

(edited 9 months ago)

Reply 2

mqb2766

21

Original post by kittytyler

This question is meant to be very straightforward but yet I am struggling with it. Someone pls help!!!

Q) A circle has radius of 5 units and its centre lies at (k,k+1) where k is a positive integer. Given that the co ordinate axes are tangents to the circle. Find the equation of the line which joins the two points where the circle intersects the co-ordinate axes. (3)

Answer is meant to be y= -4/3x + 4

As tony says, the question sounds wrong. Can you post an image of the original question?

Reply 3

kittytyler

OP

9

Original post by mqb2766

As tony says, the question sounds wrong. Can you post an image of the original question?

That was my initial thought as well, I thought the center should be (k,k). I have attached a pic.

Reply 4

mqb2766

21

Original post by kittytyler

That was my initial thought as well, I thought the center should be (k,k). I have attached a pic.

Is it from a book? I can usually have a decent guess at what the typo is, but I simply cant see what they wanted here. If the axes are tangents the centre must be k,k but that wouldnt match with the axes having intersection (not touching) points which are different, so 3,0 and 0,4. The question is "obviously" something to do with a 3-4-5 pythagorean triple, but ...?

It could be that the origin lies on the circumference (instead of the coordinate axes being tangents) and the centre is k,k+1, radius 5 and you want the two points which are the average of the two intersection points on each axis. It would give the ans, but very different from the question.

Id move on.

(edited 8 months ago)

Reply 5

kittytyler

OP

9

Original post by mqb2766

Is it from a book? I can usually have a decent guess at what the typo is, but I simply cant see what they wanted here. If the axes are tangents the centre must be k,k but that wouldnt match with the axes having intersection (not touching) points which are different, so 3,0 and 0,4. The question is "obviously" something to do with a 3-4-5 pythagorean triple, but ...?

It could be that the origin lies on the circumference (instead of the coordinate axes being tangents) and the centre is k,k+1, radius 5 and you want the two points which are the average of the two intersection points on each axis. It would give the ans, but very different from the question.

Id move on.

Ok, thank you.

Reply 6