Coordinate Geometry Core 1 tangent length help

Hi all!

I'm doing some maths revision for the core 1 exam on Wednesday and I can't seem to get the right answer for this question. The book I'm using is however frequently wrong so I was wondering whether someone else could do the question and see if we get the same answers or whether you get what's in the book. I got the length to be the square root of 57.

Find the length of the tangent from the point (2,5) to the circle x^2 + y^2 -14x - 2y+12=0

Thanks in advance

(edited 1 year ago)

Reply 1

ghostwalker

Post some working then - I get root(3)

Reply 2

TSR George

Original post by ghostwalker

Post some working then - I get root(3)

Will do, the book gets 5?

Reply 3

Bigbosshead

What was the book's answer?

I got root 3 also

Original post by ghostwalker

Post some working then - I get root(3)

The centre of the circle is (7,1) meaning when you have solved the equation of the circle into completed square form you the radius as 4.
I then worked out the length of the line from (2,5) to (7,1) using pythagoras and got that to be sqrt41 (25+16to give 41). Then I used pythagoras again to get the length by doing 41+16 = 57 and then square rooted that for the final length

Reply 6

Bigbosshead

The completed square form gave me a radius square root 38.

(edited 7 years ago)

Reply 7

username2176541

Original post by Bigbosshead

The completed square form gave me a radius 38.

38^1/2

Reply 8

TSR George

Original post by Bigbosshead

The completed square form gave me a radius 38.

But 7 squared is 49 and 1 squared is 1 and you have 34 already meaning 50-34=16? And therefore r=4?

Reply 9

username2176541

It clearly says 12 not 34. Please post the full question word for word I feel as though you missed something out

Reply 10

TSR George

Original post by Xenon17

It clearly says 12 not 34. Please post the full question word for word I feel as though you missed something out

Sorry yes, it is meant to be +34 and then that is the full question word for word, sorry, I got the 12 from the question below, oops!

lol

In which case the book's answer of 5 is correct.

Reply 13

ghostwalker

Should be 41-16 giving 25 and root.

The distance of the point (2,5) to the centre forms the hypotenuse of the triangle, hence subtracting from the 41.

Reply 14

LewisClothier

Original post by ghostwalker

Should be 41-16 giving 25 and root.

The distance of the point (2,5) to the centre forms the hypotenuse of the triangle, hence subtracting from the 41.

woah, you don't need to do this, the circle has point (7,5) at the top (because the radius is 4, and the centre is (7,1)), and the other point given was (2,5). simple as doing 7-2 = 5

(edited 7 years ago)

Reply 15

ghostwalker

Original post by LewisClothier

woah, you don't need to do this, the circle has point (7,5) at the top, and the other point given was (2,5). simple as doing 7-2 = 5

Methods that work in special situations are useful, but the OP had an issue with working out the length with the more general method, and it was important they get that right. Good spot though.