1.

If the ellipse x^(2)+k^(2)y^(2)=k^(2)a^(2) is confocal with the hyperbola x^(2)-y^(2)=a^(2), then match the following lists and choose the correct code.

Answer»


Solution :FOCUS of ellipse `-=(kae_(1),0)`
and Focus of hyperbola `-=(ae_(2),0)`
Now, `kae_(1)=ae_(2)`
`rArr""sqrt(1-(a^(2))/(k^(2)a^(2)))=sqrt(1+(a^(2))/(a^(2)))`
`rArr""k^(2)-1=2`
`therefore""k= pmsqrt3`
a. `(e_(2))/(e_(1))=k=SQRT3` ltBrgt b. Major axis of ellipse = 2ka
and
Transverse axis of hyperbola = 2A
`therefore""(2ka)/(2a)=k=sqrt3`
C. Since curves are confocal, they are orthogonal.
`therefore""theta=(pi)/(2)`
d. Latus rectum of ellipse and hyperbola are`(2a^(2))/(ak) and (2a^(2))/(a)`, respectively.
`therefore""(2a//k)/(2a)=(1)/(k)=(1)/(sqrt3)`


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