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Given A circle, 2x^(2) + 2y^(2) = 5 and ...

Given A circle, `2x^(2) + 2y^(2) = 5` and a parabola, `y^(2) = 4 sqrt(5) x`.
Statement I :- An equation of a common tangents to these curve is `y = x + sqrt(5)`
Statement II If the line, `y = mx + (sqrt(5))/(m) (m != 0)` is the common tangent, then m satisfies `m^(4) - 3 m^(2) + 2 = 0`

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 correct explanation for statement 1.

C

Statement 1 is true , statement 2 is false.

D

Statement 1 is false , statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
B
2 Tangent to parabola `y^(2)=4sqrt(5)x`, having slope m is :
`y=mx+(sqrt(5))/(m)`
This line is tangent to the circle `2x^(2)+2y^(2)=5`
`rArr` Distance of center from the line is equal to its radius.
`rArr" "|{:(mxx0-0+(sqrt(5))/(m))/(sqrt(1+m^(2))):}|=sqrt((5)/(2))`
`rArr" "m^(4)+m^(2)-2=0rArrm^(2)=1rArrm=pm1`
Also `m^(2)=1` satisfies `m^(4)-3m^(2)+2=0`
One of the common tangents for m=1 is `y=x+sqrt(5)`.
Thus, both statements are correct, statement 2 is not correct explanation of statement 1
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