The curves 4x2+9y2=72  andx2−y2=5  at(3,2)

4x2+9y2=72           Differentiating  w .r.t.  x, we have                 8x+18ydydx=0⇒dydx=−49xyAt(3,2),​​​​​​​​​​​​​​​​​​​​​​​​​dydx=−49×32=−23Also x2−y2=5⇒dydx=xyAt(3,2),​​​​​​​​​​​​​​​​​​​​​​​​​dydx=32 Hence, the curves cut orthogonally .