Question

a. Find dy/dx if y^2 + x^2 = 16 b. Find the equation of the tangent line that contains the point (2, 2 squareroot 3).

Answer 1

`x+√(3)y=8`

Explanation:

Given equation of curve,

`y^2+x^2=16`

`\implies y^2=16-x^2`

Differentiating with respect to x,

`2y(dy)/(dx)=-2x`

`\implies (dy)/(dx)=-(x)/(y)`

Since, the tangent line of the curve contains the point (2, 2√3),

Thus, the slope of the tangent line,

`m=\left [ (dy)/(dx) \right ]_((2, 2√(3)))=-(1)/(√(3))`

Hence, the equation of tangent line would be,

`y-2√(3)=-(1)/(√(3))(x-2)`

`√(3)y-6=-x+2`

`\implies x+√(3)y=8`