The figure below shows a conchoid of Nicomedes. The top part is formed by a ray from the origin that rotates through an angle t° with the
x-axis.
The ray intersects the fixed line y = 2 at point A. From A you measure out 7 more units to point P on the graph of the conchoid. The bottom part is formed when the ray is in Quadrants III and IV and you measure 7 units from where the line containing the ray intersects the fixed line.
The parametric equation for x has two parts, one for the segment from the origin to the point on the x-axis below point A, the other from there to the point on the x-axis below point P. Write an equation for x as a function of t.
x = 2 t + t
Write the parametric equation for y as a function of t. It, too, will have two parts.
y = + t
The Cartesian equation of this conchoid is
(x^2 + y^2)(y - 2)^2 = 49y^2
Verify that this equation is correct by calculating the values of x if y is 8 and showing that the points really are on the conchoid.
(Round to the nearest hundredth.)
1 answer
1 answer