What is the slope of the tangents drawn from | vedclass

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(C) The equation of the parabola is $y^2 = -12x$,where $4a = 12$,so $a = -3$.The equation of a tangent to the parabola $y^2 = 4ax$ with slope $m$ is $

Vedclass · Accepted Answer

$3, -1/3$

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(C) The equation of the parabola is $y^2 = -12x$,where $4a = 12$,so $a = -3$.The equation of a tangent to the parabola $y^2 = 4ax$ with slope $m$ is $y = mx + \frac{a}{m}$.Substituting $a = -3$,the tangent equation is $y = mx - \frac{3}{m}$.Since the tangent passes through $(3, 8)$,we have $8 = 3m - \frac{3}{m}$.Multiplying by $m$,we get $8m = 3m^2 - 3$,which simplifies to $3m^2 - 8m - 3 = 0$.Factoring the quadratic equation: $3m^2 - 9m + m - 3 = 0 \implies 3m(m - 3) + 1(m - 3) = 0$.Thus,$(3m + 1)(m - 3) = 0$,giving $m = 3$ or $m = -1/3$.

What is the slope of the tangents drawn from $(3, 8)$ to the parabola $y^2 = -12x$?

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