anonymous
  • anonymous
The circles which can be drawn to pass through (3,0) and (5,0) and to touch the y-axis, intersect at an angle theta, then what is the value of cos(theta) ?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
dumbcow
  • dumbcow
if what is drawn above is true, then angle where they meet is 180 cos(180) = -1 ?
anonymous
  • anonymous
No that is not even in the option. Option (a) 7/8 (b) 1/2 (c) 0 (d) 1/sqrt(2)
anonymous
  • anonymous
and I the question means that circles which pass through BOTH (3,0) and (5,0)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Mertsj
  • Mertsj
Did you draw a picture?
anonymous
  • anonymous
I tried...but can't understand how to take out that theta. And the diagram isn't given in the question...but I am pretty sure its talking about the circles passing through both the points.
anonymous
  • anonymous
I guess so...since both are touching the y-axis and passing through those points...
anonymous
  • anonymous
maybe going through both points and tangent to the y-axis?: |dw:1333627231016:dw|
anonymous
  • anonymous
touching the y-axis.
anonymous
  • anonymous
|dw:1333627692928:dw|
anonymous
  • anonymous
|dw:1333628244067:dw|
anonymous
  • anonymous
so, I got cos(theta) = 15/17 but it's not one of your choices so maybe this may not be the picture?
dumbcow
  • dumbcow
|dw:1333659614476:dw| note the tangent lines do not go through center of circle, so thats why it cant be a 90 degree angle slopes are found by taking derivative of the circles at point (3,0) given the slopes of the 2 lines, the angle between them is about 29 degrees cos(29) = 7/8
dumbcow
  • dumbcow
circle 1: \[(x-4)^{2}+(y-\sqrt{15})^{2} = 16\] circle 2: \[(x-4)^{2}+(y+\sqrt{15})^{2} = 16\] differentiate both equations solve for dy/dx circle1: \[\frac{dy}{dx} = \frac{4-x}{y-\sqrt{15}}\] circle 2: \[\frac{dy}{dx} = \frac{4-x}{y+\sqrt{15}}\] evaluate at point (3,0) \[\frac{dy}{dx} =- \frac{1}{\sqrt{15}}\] \[\frac{dy}{dx} = \frac{1}{\sqrt{15}}\] |dw:1333693416704:dw| \[\tan (\theta/2) = \frac{1}{\sqrt{15}}\] \[\rightarrow \theta = 28.955\] \[\rightarrow \cos \theta = \frac{7}{8}\]
anonymous
  • anonymous
How did you know the center of the circle was (4, sqrt15)?? I got the x-coordinate but how did you find out the y-coordinate..ie, \[\sqrt{15}\] ??
dumbcow
  • dumbcow
from the equation of a circle \[(x-4)^{2}+(y-k)^{2} = 16\] plug in point (3,0) or (5,0) \[1+k^{2} = 16\] \[k = \pm \sqrt{15}\]
anonymous
  • anonymous
oh yes..silly me! Thanks again! :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.