Tangents And Normals

Given equation of curve is
... (i)
Taking derivative w.r.t. ori both sides



Since, curve has tangent parallel to x-axis
slope of tangent= 0

.....(ii)
\
Now solving (i) and (ii) we get,


For and
Points are (3, 6) and (-3, -6)

The equation of normal to a curve at a point is given by the formula: where is the derivative of the curve at the point . 1. First, differentiate the equation of the curve implicitly to find the slope of the tangent at . For the given equation, , we need to differentiate both sides with respect to , considering implicit differentiation: 2. After differentiating and solving, substitute to get the slope of the normal. Finally, we can determine the equation of the normal, which is .