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A circle cuts a chord of length 4a on th...

A circle cuts a chord of length 4a on the x-axis and passes through a point on the y-axis, distant 2b from the origin. Then the locus of the centre of this circle is

A

A parabola

B

A hyperbola

C

A straight line

D

An elipse

Text Solution

Verified by Experts

The correct Answer is:
A
In `Delta ACM:`
`K ^(2) + 4a ^(2) =r ^(2) " "…(i)`
`h ^(2) + (K-2b)^(2) =r ^(2) " "…(ii)`
`K ^(2) + 4a ^(2) = h^(2) + (K -2b )^(2) `
`K ^(2) + 4a ^(2) =h^(2)+ K^(2) + 4b ^(2) -4Kb`
`therefore h ^(2) =4Kb + 4a ^(2) -4b ^(2)`
`x ^(2)=4by+ 4a ^(2) -4b ^(2)`
`therefore ` Parabola.
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