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Consider, L(1) : 2x + 3y + p – 3 = 0 , L...

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–10y+30=0`
Statement-I : If line `L_(1)` is a chord of circle C, then line `L_(2)` is not always a diameter of circle C.
and
Statement-II : If line `L_(1)` is a diameter of circle C, then line `L_(2)` is not a chord of circle C.

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statemcnt-2 is True, Statement-2 is Not a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

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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.

Condider the lines L_(1):3x+4y=k-12,L_(2):3x+4y=sqrt2k and the ellipse C : (x^(2))/(16)+(y^(2))/(9)=1 where k is any real number Statement-1: If line L_(1) is a diameter of ellipse C, then line L_(2) is not a tangent to the ellipse C. Statement-2: If L_(2) is a diameter of ellipse C, L_(1) is the chord joining the negative end points of the major and minor axes of C.

The line x+3y=0 is a diameter of the circle x^(2)+y^(2)-6x+2y=0

The line x+3y=0 is a diameter of the circle x^(2)+y^(2)+6x+2y=0

Let L_(1):2x+3y+lambda-3=0 and L_(2):2x+3y+lambda+3=0 be two lines where lambda is an integer and C:x^(2)+y^(2)+6x+10y+30=0 is a circle,then find all possible values of lambda for which both the lines are chords of the given circle

Consider circles C_(1): x^(2) +y^(2) +2x - 2y +p = 0 C_(2): x^(2) +y^(2) - 2x +2y - p = 0 C_(3): x^(2) +y^(2) = p^(2) Statement-I: If the circle C_(3) intersects C_(1) orthogonally then C_(2) does not represent a circle Statement-II: If the circle C_(3) intersects C_(2) orthogonally then C_(2) and C_(3) have equal radii Then which of the following is true?

S:x ^(2) + y ^(2) -8x + 10y =0 and L : x -y -9=0 are the equations of a circle and a line.

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