Find curves and determine the point of intersection

Question

Give equation of locus of points such that difference in distances from (1.6) and (1.-6) is 10. Find curves and determine the point(s) of intersection: x² - 9y² - 8x + 18y + 43 = 0; y³ + x² - 8x - 2y = -13 4x² + y²+ 24x - 6y - 8 = 0; 3x - 4y = 4 x² + y² + 2x - 4y - 3 = 0; x² + y² - 2x = 7.