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If theta is the angle between the lines ...

If `theta` is the angle between the lines `ax^2 +2hxy + by^2 =0` , then angle between `x^2 + 2xy sectheta + y^2 =0` is

A

`theta`

B

`2 theta`

C

`(theta)/(2)`

D

`3theta`

Text Solution

Verified by Experts

The correct Answer is:
A
Angle between the lines `ax^2+2hxy+by^2=0` is
`tantheta=|(2sqrt(h^2-ab))/(a+b)|`
For `x^2+2xysec theta+y^2=0`
`h=sec theta, a=b=1`
`therefore tan phi =|(2sqrt(sec^2theta-1))/(1+1)|`
`therefore` Angle between `x^2+2xy sec theta +y^2=0` is `theta`.
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