Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Tangent of a Circle

One of the tangent line equation of the circle

at the point whose absis is -1 is ....
A. 2x - 3y - 7 = 0
B. 2x - 3y + 7 = 0
C. 2x + 3y - 5 = 0
D. 2x - 3y - 5 = 0
E. 2x - 3y + 5 = 0

By substituting x = -1, I got:

(y + 1) (y + 7) = 0
y = -1 or y = -7
Then what?

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: [ASK] Tangent of a Circle

The easy way is to substitute x = -1 and y = firstly -1 and then -7, into the five possible answers to see which fits.

If you didn't have multi choice you could get the gradient of the radius to one point (m), then the gradient of the tangent is -1/m  so you can build the equation of the tangent.

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Tangent of a Circle

Let's try... Judging by the circle's equation, the center is (-3, 4) thus the slope you asked is either

or

and so the slope of the tangent is either

or

. Trying to substitute the first one I'll get:

5(y + 1) = 2(x + 1)
5y + 5 = 2x + 2
5y - 2x + 3 = 0
For the second one:

11(y + 7) = 2(x + 1)
11y + 77 = 2x + 2
11y - 2x + 73 = 0
Huh? Where did I go wrong? Or did I misinterpret your hint?

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: [ASK] Tangent of a Circle

Took me a while to find it. Y = +1. Or +7

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Tangent of a Circle

Why is it y = 1 or y = 7 instead of y = -1 or y = -7? Doesn't (y + 1)(y + 7) = 0 mean y + 1 = 0 or y + 7 = 0?

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: [ASK] Tangent of a Circle

Back in post 1, when you put in x=1, you changed -8y to +8y. Apart from that the working is good.

Bob

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Tangent of a Circle

Oh! I see, why didn't I realize that...

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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.