Calculus, EXT1 C3 2020 HSC 12e Find the curve which satisfies the differential equation `(dy)/(dx) = -x/y` and passes through the point `(1, 0)`. (3 marks) --- 6 WORK AREA LINES (style=lined) --- Show Answers Only `x^2+y^2=1` Show Worked Solution COMMENT: Note the answer requires a curve equation, not a function. `(dy)/(dx) = -x/y` `int y\ dy = −int x\ dx` `(y^2)/2 = -(x^2)/2 + c` `text{Curve passes through (1, 0):}` `0` `= -1/2 + c` `c` `= 1/2` `(y^2)/2` `= -(x^2)/2 + 1/2` `y^2` `= -x^2 + 1` `:.x^2+y^2` `= 1`