Let C be the intersection of a plane ax+by+cz + d = 0 with the unit sphere S². Show that a + iy is the image of a point on C' under thestereographic projection p if and only if (x, y) is a point on the curve C" defined by the equation2x2ya (₁ ²+²+² +1) 10 (2² +²²2 +1) ¹ ( ² + ² + 1)+ b+bthe curve C' is the Euclidean circle with centerc+dac+d²+ d = 0. Then show that if C does not pass through the north pole N(0, 0, 1), thenand radiusa²+6² +c² - d²(c +d)²

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Let C be the intersection of a plane ax + by+cz+d=0 with the unit sphere S². Show that x + ży is the image of a point on C under the stereographic projection p if and only if (x, y) is a point on the curve C" defined by the equation 2x 2y ª (2² +²²2 +1) +6 (2² +²3² +1) + ( 2² + ² + 1). a b b the curve C' is the Euclidean circle with center c+d a c+d' + d = 0. Then show that if C does not pass through the north pole N(0, 0, 1), then and radius a² +6² +c²d² (c + d)²