The curve passing through the point (1,2) given that the slope of the tangent at any point (x, y) is 3 x y represents

Step-by-step solution

We have, aligned d y d x &= 3 x y & y d y &= 3 x d x & & y² 2 &=3 x² 2 +C...(i) aligned Since, Eq (i) passing through point (1,2) aligned & 4 2 = 3 2 (1)²+c & c=2- 3 2 = 1 2 & Equation of curve, y² 2 = 3 x² 2 + 1 2 & y²=3 x²+1 y²-3 x²=1 & y² (1)² - x² (1 / 3 )² =1 aligned Which represents a Hyperbola.