Find the 15

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

Result

t1 = (Correct answer is: x + sqrt(19)) Wrong answer
t2 = (Correct answer is: x-sqrt(19)) Wrong answer

Solution:

9 x2+16 y2=144 (x/a)2+(y/b)2=1  a=16=4 b=3=31.7321  k=1  b2q2+a2k2=0  1.732050807572q2+42 (1)2=0 q2+19=0 q219=0  a=1;b=0;c=19 D=b24ac=0241(19)=76 D>0  q1,2=b±D2a=±762=±19 q1,2=±19=±4.35889894354 q1=19=4.35889894354 q2=19=4.35889894354   Factored form of the equation:  (q4.35889894354)(q+4.35889894354)=0  t:y=kx+q  t1=x+19
t2=x19



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