Question

Find the equation of the tangent to the curve `x^(2) + 3y = 3`, which is parallel to the line `y - 4x + 5 = 0`

Answer 1

Correct Answer - `4x - y + 13 = 0`
`x^(2) + 3y = 3 rArr 2x + 3 (dy)/(dx) = 0 rArr (dy)/(dx) = (-2x)/(3)`
`y - 4x + 5 = 0 rArr y = 4x + 5 rArr` its slope = 4
`:.` the slope of the tangent = 4
So, `(-2x)/(3) = 4 rArr x = -6`
`x^(2) + 3y = 3, x = -6 rArr y = -11`
The equation of the tangent at `(-6, -11)` with slope = 4 is `y + 11 = 4 (x +6)`