1.

The equation of common tangent to the parabola `y^2 =8x` and hyperbola `3x^2 -y^2=3` is

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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