circles

1. Circles

Find the equation of a circle with centre on the y-axis, which cuts orthogonally each of the circles x2+y2+6x+2y-9=0 and x2+y2-2x-2y+1=0. (x+3)2+(y+1)2=10, (x-1)2+(y-1)2=1 I tried to use ratio to solve it. Like 32+(y-1)2 : 1+(y-1)2 = 3:2 y2-2y+10=3y2-6y+6 y2-2y-2=0 y=1+sqrt3 hence the equation...
2. Another tough Geometry Question ( Pythagoras and Circles and Tangents)

Hi guys, another tough problem thats giving me some trouble. I thought i might look to the geniuses on this forum for help. Anyway, i am attaching a picture, basically i have to find the radius of the circle using phythagoras. The smaller circle has a radius of 1cm and the angle between the...
3. Circles

Through any given set four points P,Q,R,S how many circles can be drawn ? How can we solve this using combinatoric analysis ?
4. Help needed calculating the area of a rectangle with 2 semi circles on either side

I start University in 3 months and im going over past papers for Mathematics. I have had a good deal of success with all questions bar one. As i have finished up college i have no lecturers to ask how you would approach this and tbh its annoying me. I have spent 2 days and i feel i have hit a...
5. Distance between center of two circles

I have to find O1O2 but I've no idea how.. Any advices ? Thank you!
6. halp solving trig formula using unit circles

Hi, I'm working on some practice questions using unit circles in advance of a chapter quiz tomorrow and am stuck on one question that I must have a mental block about. The question is as follows: Solve the equation on the interval theta is greater than or equal to zero and less than pi...
7. Points on circles collinear

Last one... Diagonals of quadrilateral $ABCD$ intersect in point $S$. Circle $k_1$ is circumscribed of triangle $ABS$. $k_1$ intersects line $BC$ in point $M$. Circle $k_2$ is circumscribed of triangle $ADS$ and it intersects line $CD$ in point $N$. Prove that points $S, M$ and $N$ are collinear.
8. How to plot circles in MathGV

I cannot plot a circle because it considers 'y' as an invalid character when it try to enter 'x^2 + y^2 = 1 How then do I plot circles, I cannot find it in the help library
9. Radical Axis of 3 circles...

Can someone help me with this. Suppose you have 3 circles and you find the radical axis of each of these. Apparently the 3 radical axes intersect at a unique point. Q1: why? and Q2: Apparently there is a unique circle ( centre point intersection of radical axes) which is orthogonal to each...
10. Circles

3. A small radio transmitter broadcasts in a 50 mile radius. If you drive along a straight line from a city 60 miles north of the transmitter to a second city 70 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter? I am completely lost on...
11. Intro to Circles Problem (Circles, Points, Substituion, Graph of the equation)

Center of the circle is O=(2,4). Verify by substitution that point A=(5,8) is on the circle that is the graph of the equation (x-2)^2+(y-4)^2=25
12. Plane defined by Circle

Given three points that are not colinear, how do you define a plane such that the circle intersecting these three points lies on the plane? Please define the plane as a function f(x,y) = \alpha x + \beta y + \gamma.
13. Help with unit circles

Hi. I am having trouble proving that cos(theta + pi/2) = -sin theta, using a unit circle. I was hoping someone could help me out here using a unit circle diagram to show. Thanks, Jono
14. Circles related angles and segments.

Hey Guys, I'm having some trouble with this problem. so far I know that XY = 10. I looked at the whole triangle first. Triangle XYZ. I know that XZ is 6 so I applied the pythagoreans theorem which got me YZ = 8. From this step I don't know what to do. I've tried looking at it different ways...
15. Two non-intersecting circles...

Two non-intersecting circles C1, containing points M and S, and C2, containing points N and R, have centres P and Q where PQ=50. The line segments [MN] and [SR] are common tangents to the circles. The size of the reflex angle MPS is α, the size of the obtuse angle NQR is β, and the size of the...
16. Area between two circles

Find the area of the region between the circles x^2 + y^2 = 4 and x^2 + y^2 = 4x My attempt at the solution: I found the points of intersection are at (1,-sqrt(3)) and (1, sqrt(3)) Then I solved for x in each equation: x=sqrt(4-y^2) , x=sqrt(y^2+4) + 4 This is where I get stuck. I don't know...
17. Circles and Angles

I'm hoping that someone can give me some help with the following problem: O is the centre of the circle (show on the attachment to this post) and AB is parallel to CD. Find the angles labelled x and y. With a bit of cheating I was able to find that x = 32o and y = 58o but my questions is 'why'...
18. Equations of Circles

Circle C1 has points B(4,2) and E(10,12) on its circumference. Equation of circle and radius are not known. Show that Circle C1 has its centre O at (2,10) Please advise (I read that you can find the centre with 3 points, or 2 points + radius known, but this case has no radius?)
19. different circles

If three different circles are drawn on a piece of paper, at most how many points can be common to all three? A) Non B) one C) two D) three E)six E is the correct answer I could get four...but I cant get six at all! So is that enough reason to choose E?
20. Identifying Ellipses,Circles and Parobolas w/Picture

How can you tell if its an ellipse, circle or a parobola? I noticed that the Parobla only has one term with a degree of 2 . I noticed that the circle has same coefficients with their terms like y=x^2 +y^2 another example of cirlce y=9x^2 +9x^2 The Ellipse has different number coefficents...