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Given pair of lines 2x^(2) +5xy +2y^(2) ...

Given pair of lines `2x^(2) +5xy +2y^(2) +4x +5y +a = 0` and the line `L: bx +y +5 = 0`. Then

A

`a = 2`

B

`a =- 2`

C

There exists no circle which touches the pair of lines and the line L if `b = 5`.

D

There exists no circle which touches the pair of lines and the line L if `b =- 5`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`2x^(2) +5xy +2y^(2) +4x 5y +a =0` represents the pair of lines if
`|{:(2,5//2,2),(5//2,2,5//2),(2,5//2,a):}| =0`
`rArr a = 2`
So pair of lines is `2x^(2)+5xy +2y^(2) +4x +5y +2 =0`
or `x +2y +1 = 0, 2x +y +2 =0`
These lines are concurrent with `bx +y +5 =0`
If `|{:(1,2,1),(2,1,2),(b,1,5):}| =0`
`rArr b =5`
Which lines are concurrent, no circle can be drawn touching all three lines.
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