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ANALYTIC GEOMETRY (Conic Section; Parabola)

Find the equation of the line tangent to y^2=-16x and parallel to x+y=1.

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Find the equation of the line tangent to y^2=-16x and parallel to x+y=1.

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dy/dx = -8/y = -1

y = 8

Substituting y to the eq of parabola, we will get x = -4

The tangent line passes through point

Using point-slope formula, we have

y-8 = -1(x+4)

Therefore, the equation of the tangent line is