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Statement1: 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 theparabola `y^2=""16sqrt(3)x`and the ellipse `2x^2+""y^2=""4`, then m satisfies `m^4+""2m^2=""24`.(1)Statement 1 isfalse, statement 2 is true(2)Statement 1 istrue, statement 2 is true; statement 2 is a correct explanation for statement1(3)Statement 1 istrue, statement 2 is true; statement 2 is not a correct explanation forstatement 1(4)Statement 1 istrue, statement 2 is false |
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Answer» `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 ` `y= 2x + 4sqrt3/2` so, option 1 is correct |
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