# ANALYTIC GEOMETRY (Conic Section; Parabola)Find the equation of the line tangent to y^2=-16x and parallel to x+y=1.

1
by noimeballeser91

2014-05-15T12:57:13+08:00

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m = -1 since it is parallel to the given line. Since the equation for the slope of the tangent line its derivative, then dy/dx = m = -1

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 (-4, 8)

Using point-slope formula, we have
y-8 = -1(x+4)

Therefore, the equation of the tangent line is y = -x + 4
how to get the point of tangency (-4,8) without using derivative or any calculus lessons.
I'm not really sure. So far, that is the only way I can think of.