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Question : 8 of 160
Marks:
+1,
-0
Solution:
Given,
Focus
(S)=(1,2) Eccentricity
(e)=√3 Equation of Directrix is
2x+y=1 Required equation of hyperbola is
SP=ePM √(x−1)2+(y−2)2=√3‌ Squaring on both sides.
(x−1)2+(y−2)2=‌(2x+y−1)2 ⇒x2+1−2x+y2+4−4y =‌(4x2+y2+1+4xy−2y−4x) ⇒‌‌5(x2+y2−2x−4y+5) =3(4x2+y2+4xy−4x−2y+1) 5x2+5y2−10x−20y+25 =12x2+3y2+12xy−12x−6y+3 ⇒5x2+5y2−10x−20y+25−12x2 −3y2−12xy+12x+6y−3=0 ⇒‌‌2y2−7x2−12xy+2x−14y+22=0 ∴‌‌2y2−12xy−7x2+2x−14y+22=0
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