Geometric Analysis

dress 1\nThe equivalence of the great deal is: x2 + 32x + y2 -24y = 0. When, x=0, y2 = 24y, therefore(prenominal), y = sqrt(24) = 4.898. When y=0, x2 = 32x, thereforecece x = sqrt(32) = 5.656. First, we approximate the comparison for stage business OA. This has 2 points, O and A. The coordinates atomic number 18 (-5.655, 4.898) and (-34.794, 18.840). set up is disposed by m = y2-y1/x2-x1 = 18.84+5.655/-34.794-4.898 = 24.495/-39.692= -0.617. The equality of the concern produces, y = mx + b, then y = -0.617x + b. Here, we gull 18.84 = -0.617(-34.794) + b, then, b = 18.84 - 21.468 = -2.628. The equating 1 is y = -0.617x -2.628.\nNow, we cipher blood OB. The coordinates atomic number 18 (-5.655, 4.898) and (-7.548, 30.126). set up is apt(p) by m = y2-y1/x2-x1 = 30.126-4.898/-7.548-5.655 = 25.228/-18.102= -1.394. The equation of the inception becomes, y = mx + b, then y = -1.394x + b. Here, we drive home 30.126 = -1.394(-7.548) + b, then, b = 30.126-10.522 = 19.6 04. The equation 2 is y = -1.394x + 19.604.\nNow, we lease the convergency point. then(prenominal), equating 1 and 2, we get, -0.617x -2.628 = -1.394x + 19.604. Then, we have, 0.777x = 22.232, then, x = 28.613. Then, y becomes, y = -1.394(28.613) + 19.604 = -20.282. Then, the coordinates of C become disallow of these as we employ the erect lines and non the tangent lines. Then, C is (-28.613, 20.282).\n issue 2\nWe know, d2 = (x1-x2)sq + (y1-y2)sq, then, 39.498 = (63.983-x2) + (43.917-y2), when x=0, 39.498 = 43.917-y2, then y2 = 4.419. Likewise, when y2 = 0, 39.498 = 63.983-x2, then x2 = 24.485. Then P is (24.485, 4.419).