This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Okay, cloths, let's find where the locus meets the y-axis. Step 1: Set x=0 in the equation of the locus. The equation of the locus is 3x^2 + 3y^2 + 12x - 38y + 55 = 0. Substitute x=0: 3(0)^2 + 3y^2 + 12(0) - 38y + 55 = 0 0 + 3y^2 + 0 - 38y + 55 = 0 3y^2 - 38y + 55 = 0 Step 2: Solve the quadratic equation for y. We can use the quadratic formula y = -b ± sqrt(b^2 - 4ac)2a, where a=3, b=-38, and c=55. y = -(-38) ± sqrt((-38)^2 - 4(3)(55))2(3) y = 38 ± sqrt(1444 - 660)6 y = 38 ± sqrt(784)6 y = (38 ± 28)/(6) Step 3: Calculate the two possible values for y. y_1 = (38 + 28)/(6) = (66)/(6) = 11 y_2 = (38 - 28)/(6) = (10)/(6) = (5)/(3) Step 4: State the points where the locus meets the y-axis. Since x=0 for both points, the points are (0, y_1) and (0, y_2). The points are (0, 11) and (0, (5)/(3)). What's next?