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The equation of common tangent to the parabola `y^2 =8x` and hyperbola `3x^2 -y^2=3` is |
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Answer» `a^2=1` so, `a=+-1` `b^2=3` so,`b=+-sqrt3` equation of tangent to hyperbola `y=mx+-sqrt(a^2m^2-b^2)` `y=mx+-sqrt(m^2-3)` -(1) equation of parabola`y^2=8x` so, 4a=8 a=2 equation of tangent to parabola `=y=mx+a/m` `=y=mx+2/m` -(2) tangent is common so equation(1) and (2) will be equal `mx+-sqrt(m^2-3)=mx+2/3` `+-2/m=sqrtm^2-3` squaring both side `4/m^2=m^2-3` `4=m^4-3m2` (t-4)(t+1) t=4,-1 but -1 is not possible `m^2=4` `m=+-2` equation of tangent `y=mx+2/m` when m=2 `y=2x+1` whrn m=2 y+-2x-1 |
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