Question

Line intersecting circle on coordinate plain question, PLEASE HELP!
Since I can't put pictures on here, here's the link -> http://www.math.washington.edu/~m120/TheBook/TB2010-11.pdf It's in the chapter four exercises and is question 4.7! I don't even need the answers, I would just like simple guidance on how to do them (described so) so I can do it myself! Please and thank you!!

Answer 1

The cup on the 9th hole of a golf
course is located dead center in the middle of a
circular green that is 70 feet in diameter. Your
ball is located as in the picture below

Answer 2

This one?

Answer 3

Yes! I'm stuck on the equation of the line intersecting the circle!

Answer 4

If the diameter is 70, then the radius is 35.
That would mean the equation of the circle is \[
x^2+y^2=35^2
\]

Answer 5

Right, and to find where it first touches the green part, we'd need the line's formula for it but we don't know where it exactly touches it at first?

Answer 6

cute text book

Answer 7

The slope here is \[
m = \frac{50}{40+35}=\frac{50}{75}=\frac 23
\]

Answer 8

also \[
(0) = \frac 23 (35)+b\implies b = -\frac{70}{3}
\]

Answer 9

Where do we get -70/3 from?

Answer 10

I solved for \(b\)... look at the part before the arrow.

Answer 11

Since \[
y = \frac 23 x-\frac{70}{3}
\] We use substitution:\[
x^2+\left( \frac 23 x-\frac{70}{3}\right)^2=35
\]This will expand into a quadratic equation.