how to find the slope of the curve 17x^2+12xy=100-8y^2 at the point where y=1.

Question

-i already d/dx but i didn't know how to find the slope of curve bcus they only give y.
d/dx=(-34x-12y)/(12x+16y)

Answer 1

Given y=1, substitute in original equation and solve for x:
17x^2+12xy=100-8y^2, or
17*x^2+12*x-92=0
which gives
x=-46/17 or x=2

So substitute
(-46/17,1) and (2,1) into your expression for dy/dx to get the numerical value.