Let C be a unit circle centered at (2,0)
Let l be any line through the origin and intersecting C at points A1 and A2.
The locus P is the set of points on line l with OB=A1A2.
Find parametric equations for the locus of P.
(In reply to
re(2): what the curve looks like by Charlie)
Although the curve fits on the x-axis, it doesn't fit vertically. This program finds the points of intersection of the line with the circle and the distance between them. It uses that to find a point on the locus sought. Then evaluates the LHS and the RHS of the proposed equation in my previous post, and they don't match.
syms x y
for angle=0:5:25
slope=tand(angle);
eqns=[y==slope*x, (x-2)^2+y^2==1];
S = solve(eqns,[x y]);
dist=double(sqrt((S.x(1)-S.x(2))^2 + (S.y(1)-S.y(2))^2));
x1=dist*cosd(angle);
y1=dist*sind(angle);
LHS = (x1^2+2*y1^2)^2;
RHS = 4*(x1^2-2*y1^2);
disp([angle LHS RHS])
end
angle LHS RHS
0 16 16
5 15.2718645233653 15.1603127783735
10 13.1305335227521 12.7973618034191
15 9.76159824632146 9.35898384862246
20 5.65167818914667 5.52577853924721
25 1.81258532668361 2.1209393485321
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Posted by Charlie
on 2021-07-04 09:19:30 |
Well, that's not the curve
