If tangent drawn to the parabola y^2=-a x(a0) from a point A(1,0) which also touches the hyperbola x^2 4 - y^2 b^2 =1 at B such that A S B=90^ , where S is the focus of the hyperbola then find the value of (a+b^2 ) .

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If tangent drawn to the parabola y^2=-a x(a>0) from a point A(1,0) which also touches the hyperbola x^2 4 - y^2 b^2 =1 at B such that A S B=90^ , where S is the focus of the hyperbola then find the value of (a+b^2 ) .

Quantrex Academy · Accepted Answer

Correct answer: 28

Tangent to the parabola aligned y & =m x- a 4 m (1,0) a & =4 m^2 aligned (1,0) lies on the directrix of the hyperbola 2 e =1 e=2 1+ b^2 4 =4 b^2=12 Tangent to the hyperbola aligned & y=m x 4 m^2-b^2 & a^2 16 m^2 =4 m^2-b^2 & m^2=4 m^2-b^2 3 m^2=12 m^2=4 & a=16 & a+b^2=28 & aligned

If tangent drawn to the parabola y^2=-a x(a>0) from a point A(1,0) which also touches the hyperbola x^2 4 - y^2 b^2 =1 at B such that A S B=90^ , where S is the focus of the hyperbola then find the value of (a+b^2 ) .

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