How to draw anti-aliased circle in OpenGL?

Calc question? Draw the unit circle and plot the point P=(4,2). Observe there are TWO lines tangent to the circle passing through the point?

• Draw the unit circle and plot the point P=(4,2). Observe there are TWO lines tangent to the circle passing through the point P. Answer the questions below with 3 decimal places of ...show more

• Answer:

  Two approaches I can think of for this one: 1. A. draw the right triangle from the point P to the origin. You know the length of the legs, so the cosine of the angle next to the origin is known. B. Draw a right triangle to the unknown point P from the origin - I.e., the hypotenuse connects the origin to L1. The legs, x1 and y1, are your unknowns. The hypotenuse is length 1. You need to find an interior angle of this triangle. C. The hypotenuse needs to intersect the line L1 at a 90 deg angle. Note you have a third right triangle - comprised of the points P, (0,0), and (x1,y1). The base is length 1. The hypotenuse is sqrt(20). From A and D, now you can find an interior angle for B - given that and hyp=1, now you can compute the legs x1 and y1. 2. A) dy/dx=0 at the tangent point L1=(x1,y1). B) write the equation for the upper half of the circle. C) INTEGRATE B, get an equation y=f(x). The constant, C, from the integral is probably zero, or can be figured out from