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Let C be the locus of a point the sum o...

Let C be the locus of a point the sum of whose distances from the points `S(sqrt3,0) and S'(-sqrt3,0) " is " 4.`
Statement-1: The curve C cuts off intercept `2sqrt3` from the line 2y-1=0
Statement-2: The equation of the centre C is `x^(2)+ 8y^(2)=5`

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-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:
C
The curve C represents an ellipse having its foci at `S'(sqrt3,0) and S'(-sqrt3, 0)` and major axis of length 4.
`therefore 2a=4 and 2ae =2sqrt3rArra=2 and ae=sqrt3rArra=2,e=(sqrt3)/(2)`
`therefore b^(2)=a^(2)(1-e^(2))rArr b^(2)=4(1-(3)/(4))=1`
Hence, the equation of C is `(x^(2))/(4)+y^(2)=1`.
So, statement-2 is not true.
Solving `2y-1 0 and (x^(2))/(4)+(y^(2))/(1)=1`, we gert `P(sqrt3,1//2) and Q(-sqrt3,1//2)` as point of intersection
Clearly, `PQ=2sqrt3`
So, statement-1 is true.
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