A vector of magnitude 10 along the normal to the curve `3x^2+8x y+2y^2-3=0` at its point `P(1,0)` can be `6 hat i+8 hat j` b. `-8 hat i+3 hat j` c. `6 hat i-8 hat j` d. `8 hat i+6 hat j`

Options

A. `6hati + 8hatj`
B. `-8 hati + 3hatj`
C. `6hati - 8 hatj`
D. `8 hati + 6 hatj`

Answer

a

Explanation

Differentiate the curve
`6x + 8 ( xy_(1) + y) + 4 yy_(1) =0`
`m_(T)at (1,0) is 6 + 8 (y_(1)(0)) =0`
` y_(1) (0) = -3/4`
`m_(N)= 4/3`
Unit vector =` +- (3hati + 4hatj) / 5`
Again normal of magnitude ` 10 =+- (6hati + 8hatj)`