The tangent line

Find the tangent line of the ellipse 9x2 + 16y2 = 144 with 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​=3​≐1.7321  k=−1  b2−q2+a2⋅ k2=0  1.73205080756892−q2+42⋅ (−1)2=0 −q2+19=0 q2−19=0 q1,2​=±19​=±4.358898944 q1​=4.358898944 q2​=−4.358898944  t: y=kx​+q  t1​=x+19​

Our quadratic equation calculator calculates it.

t2​=x−19​

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