Consider: `L_1:2x+3y+p-3=0` `L_2:2x+3y+p+3=0` where `p` is a real number and `C : x^2+y^2+6x-10 y+30=0` Statement 1 : If line `L_1` is a chord of circle `C ,` then line `L_2` is not always a diameter of circle `Cdot` Statement 2 : If line `L_1` is a a diameter of circle `C ,` then line `L_2` is not a chord of circle `Cdot` Both the statement are True and Statement 2 is the correct explanation of Statement 1. Both the statement are True but Statement 2 is not the correct explanation of Statement 1. Statement 1 is True and Statement 2 is False. Statement 1 is False and Statement 2 is True.

Options

A. Statement I is true, Statement II is also true,
Statement II is the correct explanation of Statement I.
B. Statement I is true, Statement II is true,
Statement II is not the correct explanation of Statement I
C. Statement I is true, Statement II is false
D. Statement I is false, Statement II is true.

Explanation

Equation of given circle C is
`(x-3)^(2)+(y+5)^(2)=9+25-30`
`i.e. (x-3)^(2)+(y+5)^(2)=2^(2)`
Centre = (3, -5)
If `L_(1)` is diameter, then `2(3)+3(-5)+p-3=0rArrp = 12`
`L_(1)" is " 2x+3y+9=0`
`L_(2)" is " 2x+3y+15=0`
Distance of centre of circle from `L_(2)` equals
`|(2(3)+_3(-5)+15)/(sqrt(2^(2)+3^(2)))|=(6)/(sqrt13)lt2` [radius of circle]
`therefore` `L_(2)` is chord of circle C.
Statement II is false.