<p>Could someone help me with this problem: </p>
<p>Find an equation for the family of lines tangent to the circle with center at the origin and radius 3.</p>
<p>Also, would the parametric equations of y=2 be:</p>
<p>y=2
x=t</p>
<p>I'm sort of guessing since it's been a few years since I took calculus</p>
<p>Draw a ray out from the origin at angle theta. It hits the circle at (3<em>cos(theta), 3</em>sin(theta)). The tangent line through this point is perpendicular to the ray; its slope is tan(theta - pi/2).</p>
<p>You can do some algebra and get the equation of the line from that. Take theta from 0 to 2*pi and you should have your answer. This is probably the easiest way to do the question, it could be done in cartesian/parametric too, or converted once you already have the answer.</p>
<p>As for the second question, probably - I don't see why not.</p>