A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Find the point(s) where the line through the origin with slope 7 intersects the unit circle.
anonymous
 4 years ago
Find the point(s) where the line through the origin with slope 7 intersects the unit circle.

This Question is Closed

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1a unit circle has the equation:\[x^2+y^2=1\]a line through the origin with slope 7 would have the equation:\[y=7x\]

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1substitute one into the other and solve for x.

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1do you need more help or can you solve this from here?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'm still a little confused

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i understand what to do, but why do y=7x?

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1ok, we know the equation of the straight line is \(y=7x\). so we can substitute this value of y into the first equation to get:\[x^2+(7x)^2=1\]\[x^2+49x^2=1\]\[50x^2=1\]\[x^2=\frac{1}{50}\]\[x=\pm\frac{1}{\sqrt{50}}\]

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1y=7x is the equation of a straight line through the origin with slope 7.

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1so now you have two values for x, substitute each one into the equation \(y=7x\) to get the corresponding value for y and you have then solved this question.

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1the general equation of a straight line is given by:\[y=mx+c\]where 'm' is the slope and 'c' is the yintercept. In your case, you are told that the slope is 7 (so m=7) and it passes through the origin (so yintercept is zero, therefore c=0).

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so it would be 7*1/\[\sqrt{50}\] and then 7*1/\[\sqrt{50}\]

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1correct, so the two values of y will be:\[y=\pm\frac{7}{\sqrt{50}}\]

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1\[x=\pm\frac{1}{\sqrt{50}}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh right okay. this is starting to make sense

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1so the two points where the line intersects the circle are:\[(\frac{1}{\sqrt{50}}, \frac{7}{\sqrt{50}})\quad\text{and}\quad(\frac{1}{\sqrt{50}}, \frac{7}{\sqrt{50}})\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thank you so so much! you are a saint

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.1you are very welcome  I'm glad I was able to help :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.