Given a circle,`2x^2+2y^2=5` and a parabola, `y^2=4sqrt(5)x`.
Statement 1: An equation of a common tangent to these curves is `y=x+sqrt(5)`.
Statement 2 if the line, `y=mx+(sqrt(5))/(m)(m ne 0)` is the common tangent, then m satisfies `m^4-3m^2+2=0`.

Options

A. Statement-1 is True, Statement - 2 is true, Statement-2 is a correct explanation for Statement-1`
B. Statement-1 is True, Statement - 2 is true, Statement-2 is not a correct explanation for Statement-7
C. Statement-1 is True, Statement - 2 is False.
D. Statement-1 is True, Statement - 2 is True.

Answer

B

Explanation

The equation of a tangent to `y^(2)=4sqrt5x` is `y=mx+sqrt5.m` where m is is the slope of the tangent.
If it touches the circle `2x^(2)+2y^(2)=5`, then
`|(sqrt(5)//m)/(sqrt(1+m^(2)))|=sqrt((5)/(2))`
` implies m sqrt(1+m^(2))=sqrt(2)`
`implies m^(4)+m^(2)-2=0`
`implies (m^(2)+2)(m^(2)-1)=0`
`implies m = +- 1`
Substituting these values in `y=x+sqrt5" and "y=-xsqrt5`. Also, values of m satify `m^(4)-3m^(3)+2=0.` Hence, both the statements are true. But, statement II is not a correct explanation of statement-i.