Question

3. (4 pts) Find the shortest distance from the surface xy + 3x + z2 = 9 to the origin.

Answer 1

d² = x² + y² + 72 solution 3) The given Surface equation is ny + 3x + 7²=9 Now, the distance from the origin to given Point (X,Y,Z) is given as so, from the given Surface equation 72= 9-(wy +39) put the value of z2 in distance equation, we get d² = x² + y ²49-(xy+3x) g C Scanned with CamScanner

and For shortest distance take partial derivative with resped to x and y ethal to zero. (13) pa (x240°49-ny-30) Ja 2x-y-3 2x For shortest distance, Old?) and hence 2x-y-3=0 o Also, a(d) 2y-X ay For shortest distance, 21d?) and hence 29-1=0 - ay CS Scanned with CamScanner

From equation @ Put x=2y in equation o, 2 x 2y - Y-3=0 3y=3 or, y = 1 Then, x=2 So, the required shortest distance is d =V@)2 +00'+9 -(246) is こ C Scanned with CamScanner