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Statement 1: An equation of a common t...

Statement 1: An equation of a common tangent to the parabola `y^2=16sqrt(3)x` and the ellipse `2x^2+""y^2=""4""i s""y""=""2x""+""2sqrt(3)` . Statement 2: If the line `y""=""m x""+(4sqrt(3))/m ,(m!=0)` is a common tangent to the parabola `y^2=""16sqrt(3)x` and the ellipse `2x^2+""y^2=""4` , then m satisfies `m^4+""2m^2=""24` .
(1) Statement 1 is false, statement 2 is true
(2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
(3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
(4) Statement 1 is true, statement 2 is false

Text Solution

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`y^2 = 16 sqrtx`
`2x^2 + y^2 = 4`
so,`y= mx + 4sqrt3/m`
`c^2 = a^2 m^2 + b^2`
`((4 sqrt3)/m)^2 = 2m^2 + 4`
`48/m^2 = 2m^2 + 4`
`=> 24 = m^4 + 2m^2`
2)`y= 2x + 2sqrt3 `
...
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