High school mathematics, equations of straight line and circle 1. Draw a tangent line from a point P (2,3) outside the circle (x-1) ^ 2 + (Y-1) ^ 2 = 1 to the circle and find the tangent equation 2. Find the area of the figure enclosed by the curve X ^ 2 + y ^ 2 = / X / + / Y /

High school mathematics, equations of straight line and circle 1. Draw a tangent line from a point P (2,3) outside the circle (x-1) ^ 2 + (Y-1) ^ 2 = 1 to the circle and find the tangent equation 2. Find the area of the figure enclosed by the curve X ^ 2 + y ^ 2 = / X / + / Y /

1. Center of circle (1,1), radius r = 1, distance from center of circle to tangent is equal to radius. If tangent slope does not exist, then it is perpendicular to X axis. If passing P, then x = 2 (1,1) to x = 2 distance = | 1-2 | = 1 = R, so x = 2 is tangent. If tangent slope exists, then Y-3 = K (X-2) kx-y-2k + 3 = 0 (1,1) to tangent distance = | k * 1-1-2k + 3 | / √ (k ^ 2 + 1) = 1 | K-2 |