=1 Let equation of tangent to the ellipse be y=mx±√18m2−10 or (y−mx)2=18m2−10 ∴‌y2+m2x2−2mxy−18m2+10=0 ‌m2(x2−18)−2mxy+y2+10=0 Given tangent makes α and β angles with transverse axis are complementary
‌∵‌‌α+β=‌
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2
‌tan(α+β)=‌ not defined ‌ ‌‌
tan‌α+tan‌β
1−tan‌α‌tan‌β
=‌ not defined ‌ ‌‌ And ‌m1=tan‌α‌‌m2=tan‌β ‌m1+m2=‌
2xy
x2−18
‌ and ‌m1m2=‌
y2+10
x2−18
‌∵‌‌1−m1m2=0⇒m1m2=+1 ‌‌‌‌
y2+10
x2−18
=+1 ‌⇒‌‌y2+10=+x2−18 ‌⇒‌‌y2=x2−28‌ or ‌x2−y2=28