Given : A circle, 2 x 2 + 2 y 2 = 5 and a parabola, y 2 = 4 5 x . Statement - I : An equation of a common…

Given : A circle, 2x2+2y2=5 and a parabola, y2=45x.

Statement - I : An equation of a common tangent to these curves is y=x+5.

Statement - II : If the line, y=mx+5m m≠0  is their common tangent, then m satisfies m4-3m2+2=0.
  1. Statement - I is true; Statement - II is false.
  2. Statement - I is false; Statement - II is true.
  3. Statement - I is true; Statement - II is true; Statement - II is a correct explanation for statement - I.
  4. Statement - I is true; Statement - II is true; Statement - II is not a correct explanation for statement - I.

Solution

Tangent to y2=45x will be y=mx+5m 
As tangent to x2+y2=52 will be y=mx±521+m2
Hence for common tangent

5m=521+m2
⇒m4+m2-2=0

⇒m2=1 , m2=−2 (Not Possible)

⇒m=±1
Hence common tangent is y=x+5

Both the statements are correct

The values of m also satisfy the equation in statement - II but it is not a correct explanation for statement - I. 

Asked in: JEE Main 2013 (07 Apr)

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