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JEE Main20257 Apr 2025Morning ShiftMathematicsHyperbolaActual

Consider the hyperbola x^2 a^2 - y^2 b^2 =1 having one of its focus at P (-3,0) . If the latus ractum through its other focus subtends a right angle at P and a^2 b^2= 2 - , , N .

Correct answer

1944

Step-by-step solution

aligned & f ₁ (- ae , 0) P (-3,0) & ae =3 aligned aligned & 45^ = b^2 / a 2 a e & 2 a e= b^2 a & b^2=6 a & Also a^2 e^2=a^2+b^2 & 9=a^2+6 a & a^2+6 a-9=0 & a=-3 3 2 =-3(1 2 ) & a^2 b^2=a^2 6 a=6 a^3 & =6(135 2 -189) & =810 and =1134 & + =1944 aligned

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