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If x=asecthetacosvarphi,\ \ y=bsecthetas...

If `x=asecthetacosvarphi,\ \ y=bsecthetasinvarphi` and `z=ctantheta` , show that `(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1`

A

1

B

0

C

-1

D

`a^2+b^2`

Text Solution

Verified by Experts

The correct Answer is:
A
As given :
`x=a secthetacosphi,y=b sec theta sinphi, z=ctantheta`
So, `x^2/a^2+y^2/b^2-z^2/c^2=(a^2sec^2thetacos^2phi)/a^2`
`+(b^2sec^2thetasin^2phi)/b^2-(c^2tan^2theta)c^2`
`=sec^2theta(cos^2phi+sin^2phi)-tan^2theta=sec^2theta-tan^2theta=1`
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