Binomial Theorem

Question
CBSEENMA11015504

Statement I An equation of a common tangent to the parabola straight y squared space equals space 16 space square root of 3 straight x end root and the ellipse 2x2 +y2 =4 is space straight y space equals 2 straight x space plus 2 square root of 3.
Statement II If the line straight Y space equals space mx space plus fraction numerator 4 square root of 3 over denominator straight m end fraction comma space left parenthesis straight m space not equal to 0 right parenthesis is a common tangent to the parabola straight y squared space equals space 16 space square root of 3 straight x and the ellipse 2x2 +y2 =4, then m satisfies m4 +2m2 =24

  • Statement 1 is false, statement 2 is true

  • Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

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

  • Statement 1 is true, statement 2 is false

Solution

C.

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

straight y squared space equals space 16 space square root of 3 straight x
straight x squared over 2 plus straight y squared over 4 space equals 1
straight y space equals space mx space plus fraction numerator 4 square root of 3 over denominator straight m end fraction space is space tangent space to space parabola
which space is space tangent space to space ellipse
rightwards double arrow space straight c squared space equals space straight a squared straight m squared space plus straight b squared
rightwards double arrow space 48 over straight m squared space equals space 2 straight m squared space plus 4
rightwards double arrow straight m to the power of 4 space plus 2 straight m squared space equals space 24
rightwards double arrow space straight m squared space equals space 4

Sponsor Area

Some More Questions From Binomial Theorem Chapter