Tangents to ellipse

Find the magnitude of the angle at which the ellipse x2 + 5 y2 = 5 is visible from the point P[5, 1] .

Correct result:

A =  26.5651 °

Solution:

x2+5 y2=5 P0=5;P1=1  x2/5+(y/1)2=1 a=5=52.2361 b=1 x0=0 y0=0  p1,p2:y=kx+q b2q2+a2 k2=0  1q2+5 k2=0 P1=k P0+q  1(P1kP0)2+5k2=0  1(1k 5)2+5 k2=0 20k2+10k=0 20k210k=0  a=20;b=10;c=0 D=b24ac=1024200=100 D>0  k1,2=b±D2a=10±10040 k1,2=10±1040 k1,2=0.25±0.25 k1=0.5 k2=0   Factored form of the equation:  20(k0.5)k=0   q1=P1k1 P0=10.5 5=32=1.5 q2=P1k2 P0=10 5=1  φ1=180πarctan(k1)=180πarctan(0.5)26.5651 φ2=180πarctan(k2)=180πarctan(0)=0  A=φ1φ2=26.56510=26.5651=263354"

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