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Find the equations of the tangent and...

Find the equations of the tangent and the normal to the curve `x^(2//3)+y^(2//3)=2` at `(1,\ 1)` at indicated points.

Text Solution

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Equation of the given curve,
`x^(2/3)+y^(2/3) = 2`
Differentiating it w.r.t. x,
`2/3x^(-1/3)+2/3y^(-1/3)dy/dx = 0`
`=>dy/dx = -(x/y)^(-1/3) = -(y/x)^(1/3)`
`:. ` Slope of the tangent at point `(1,1) = m_1 = dy/dx = -(1)^(1/3) = -1`
Let slope of the normal is `m_2`. then,
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