Find the equations of the tangent and normal to each of the following conics, the lengths of the subtangent and subnormal, then trace the curve showing these lines.
y = x2 – 6x + 4 at (4, -4).
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Expert's answer
2021-11-30T13:07:14-0500
y=x2−6x+4
y′=2x−6
Point (4,−4)
slope=m1=y′(4)=2(4)−6=2
Tangent line is
y−(−4)=2(x−4)
The equation of the tangent line in slope-intercept form
y=2x−12
Find the equation of the normal at the point (4,−4)
slope=m2=−m11=−21
y−(−4)=−21(x−4)
The equation of the normal line in slope-intercept form
y=−21x−2
TA is defined to be the subtangent at P. AN is called the subnormal.
The lengths PT and PN are called the tangent and normal.
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