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Statement 1: An equation of a common ...

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

A

Statement 1 is false 2 is true

B

Statement 1 is true, statement 2 true , statemens 2 is a correct explanation for statement 1

C

Statement 1 is true, statement 2 is true: statement 2 is not a correct explanation for statement 1

D

Statement 1 is true, statement 2 is false.

Text Solution

Verified by Experts

Equation of tangent to the ellipse `(x^(2))/(2)+(y^(2))/(4)=1` is
`y=m x(4sqrt(3))/(m) " "(1)`
Equation of tangent to the parabola `y^(2)=16sqrt(3)x` is
`y=m x+(4sqrt(3))/(m)" "(2)`
On comparing (1) and (2)
`rArr48=m^(2)(2m^(2)+4)rArrm^(4)+2m^(2)-24=0`
`rArr(m^(2)+6)(m^(2)-4)=0rArr m^(2)=4rArr m=+-2`
So, equation of commn tangents are
`y=+-2x+-2sqrt(3)`
Statement 1 is true
Statement 2 is obviously true and correct explanation of statement 1
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