The tangent line

Find the tangent line of the ellipse 9x2 + 16y2 = 144 that has the slope k = -1.

Correct answer:

t1 = x + sqrt(19)
t2 = x-sqrt(19)

Step-by-step explanation:

9 x2 + 16 y2 = 144 (x/a)2 + (y/b)2 = 1  a=16=4 b=3=31.7321  k=1  b2q2+a2 k2=0  1.73205080756892q2+42 (1)2=0 q2+19=0 q219=0 q1,2=±19=±4.358898944 q1=4.358898944 q2=4.358898944  t: y=kx+q  t1=x+19

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