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If m1 and m2 are the slopes of tangents ...

If `m_1` and `m_2` are the slopes of tangents to `x^2+y^2= 4` from the point `(3,2)`, then `m_1- m_2` is equal to

A

`(5)/(12)`

B

`(12)/(5)`

C

`(3)/(2)`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of pair of tangent is ` SS_(1)=T^(2)`
`implies (x^(2)+y^(2)-4)(9+4-4)=(3x +2y-4)^(2)`
`= 5y^(2)+16y-12xy+ 24 x-52=0`
`:. m_(1)+m_(2)=(-2h)/(b)=(12)/(5)`
and `m_(1)m_(2)=0`
Now, `m_(1)-m_(2)=sqrt((m_(1)+m_(2))^(2)-4m_(1)m_(2))`
`sqrt(((5)/(5))^(2)-0)`
`=(12)/(5)`
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