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2x+y=0 is the equation of a diameter of ...

`2x+y=0` is the equation of a diameter of the circle which touches the lines `4x-3y+10=0 and 4x-3y-30=0.` The centre and radius of the circle are

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The correct Answer is:
Radius =4 units; Centre C (1,-2)
Lines `4x-3y+10=0` and `4x-3y-30=0` are two parallel tangents.
Diameter is distance between these two lines, which is `(|10-(-30)|)/(sqrt((4)^(2)+(-3)^(2)))=8` units.
`:. ` Radius `=` 4 units.
Centre lies on the line `2x+y=0`, so let the centre be `C(h,-2h)`.
Now, distance of C from any of tangent lines is 4.
`:. (|4h+6h+10|)/(sqrt((4)^(2)+(-3)^(2)))=4`
`:. |h+1|=2`
`:. h=1`
Therefore, centre is C(1,-2) (as centre lies between the given lines).
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