Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2018-03-31 01:44:53

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,160

A circle L is going through the point O (0, 0) and P (6, 0). The center is in the line

. The equation of the circle L is ....
A.

B.

C.

D.

E.

Since the equation of a circle is

, I substituted both known points to the equation and got C = 0 as well as B = -6, so the answer is obviously B. But then my student asked "What if all options have -6 as their B? How would we know the answer?". I think it has something to do with that
, but how? Please give me some hints.

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

Offline

## #2 2018-03-31 04:59:15

bob bundy
Registered: 2010-06-20
Posts: 8,322

OP is a chord so the centre also lies on x=3.  Intersect that with the other line to determine the centre and then the radius.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

## #3 2018-03-31 12:14:13

Monox D. I-Fly
Member
From: Indonesia
Registered: 2015-12-02
Posts: 1,160

Okay, I found the center (3, 4) and the radius 5 by Pythagoras. That means the equation is:

Last edited by Monox D. I-Fly (2018-03-31 12:16:46)

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away. May his adventurous soul rest in peace at heaven.

Offline

## #4 2018-03-31 19:54:21

bob bundy
Registered: 2010-06-20
Posts: 8,322

Yes.

B

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline

## #5 2018-03-31 23:50:53

Alg Num Theory
Member
Registered: 2017-11-24
Posts: 164
Website

Monox D. I-Fly wrote:

A.

B.

C.

D.

E.

The only one of these that has the point (6,0) lying on it is B – so that must be the answer. No need for any working.

See? If you use your brain a little bit more, you can save yourself a whole lot of time and hard work for nothing.

Offline

## #6 2018-04-01 00:47:16

bob bundy
Registered: 2010-06-20
Posts: 8,322

In post 1, Monox does exactly that but then goes on to ask what if one couldn't deduce an answer from the multi choice answers.  I think it's worth considering such things as it improves one's techniques.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline