This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
a) Find the equation of the locus of S expressed in its simplest form, and state its constant properties. From our previous conversation, we found: The equation of the locus of S is 3x^2 + 3y^2 + 12x - 38y + 55 = 0. The constant properties are: Center: (-2, (19)/(3)) Radius: sqrt(232)3 = 2sqrt(58)3 b) Find the points in which the locus meets the y-axis. From our previous conversation, we found: The points are (0, 11) and (0, (5)/(3)). c) Find the equation of the tangent to the parabola 3y^2 = 16x at the point (3, 4). Step 1: Verify the point lies on the parabola. Substitute (3, 4) into 3y^2 = 16x: 3(4)^2 = 3(16) = 48 16(3) = 48 Since 48 = 48, the point (3, 4) lies on the parabola. Step 2: Differentiate the equation of the parabola implicitly with respect to x. 3y^2 = 16x (d)/(dx)(3y^2) = (d)/(dx)(16x) 6y (dy)/(dx) = 16 (dy)/(dx) = (16)/(6y) = (8)/(3y) Step 3: Find the slope of the tangent at the point (3, 4). Substitute y=4 into the derivative: m = (dy)/(dx)|_(3,4) = (8)/(3(4)) = (8)/(12) = (2)/(3) Step 4: Use the point-slope form to find the equation of the tangent. The point-slope form is y - y_1 = m(x - x_1). Using (x_1, y_1) = (3, 4) and m = (2)/(3): y - 4 = (2)/(3)(x - 3) Multiply by 3 to clear the fraction: 3(y - 4) = 2(x - 3) 3y - 12 = 2x - 6 Rearrange into the general form Ax + By + C = 0: 2x - 3y + 12 - 6 = 0 2x - 3y + 6 = 0 The equation of the tangent is 2x - 3y + 6 = 0. Got more? Send 'em.