assuming a and b are constants
take derivitive
2x+y+x(dy/dx)+2ay(dy/dx)=0
2x+y=-x(dy/dx)-2ay(dy/dx)
[tex] \frac{2x+y}{-x-2ay}= \frac{dy}{dx} [/tex]
at (1,3) the slope is -5/14
[tex] \frac{2(1)+(3)}{-1-2a(3)}= \frac{-5}{14} [/tex]
[tex] \frac{2+3}{-1-6a}= \frac{-5}{14} [/tex]
[tex] \frac{5}{-1-6a}= \frac{-5}{14} [/tex]
[tex] \frac{-5}{1+6a}= \frac{-5}{14} [/tex]
1+6a=14
6a=13
a=13/6
sub back
x^2+xy+(13/6)y^2=b
a point is (1,3)
1+(1)(3)+(13/6)(3)^2=b
1+3+39/2=b
8/2+39/2=b
47/2=b
a=13/6
b=47/2
