3. Let p be a positive real number and let I be the locus of points...

 

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3. Let p be a positive real number and let I be the locus of points satisfying |zp| = cx where z = x+iy, and c E R is a constant. (a) (4 points) Show that I is an ellipse (not necessarily centered at the origin) if 0 < c < 1 (b) (4 points) Show that I is a horizontal parabola if c = 1 (c) (2 points) Show that I is a hyperbola if c > 1 3. Let p be a positive real number and let I be the locus of points satisfying |zp| = cx where z = x+iy, and c E R is a constant. (a) (4 points) Show that I is an ellipse (not necessarily centered at the origin) if 0 < c < 1 (b) (4 points) Show that I is a horizontal parabola if c = 1 (c) (2 points) Show that I is a hyperbola if c > 1

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