Consider circles `C_1 : x^2 +y^2 + 2x-2y + p = 0, C_2 : x^2+y^2-2x+2y-p=0 and 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 statements is true ?

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?

Consider three circles C_(1), C_(2) and C_(3) as given below: 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-1: If the circle C_(3) intersects C_(1) orthogonally , then C_(2) does not represent a circle. Statement-2: If the circle C_(3) intersects C_(2) orthogonally, then C_(2) and C_(3) have equal radii.

If circles x^(2) + y^(2) + 2gx + 2fy + c = 0 and x^(2) + y^(2) + 2x + 2y + 1 = 0 are orthogonal , then 2g + 2f - c =

Consider the circles C_(1):x^(2)+y^(2)-4x+6y+8=0;C_(2):x^(2)+y^(2)-10x-6y+14=0 Which of the following statement(s) hold good in respect of C_(1) and C_(2)?

The centre of the circle that cuts the circle x^(2)+y^(2)+2gx+2fy+c=0 and lines x=g and y=f orthogonally is

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.

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.

When the circles x^(2)+y^(2)+4x+by+3=0 and 2(x^(2)+y^(2))+6x+4y+C=0 intersect orthogonally,then find the value of c is

If x^(2)+y^2-4x+6y+c=0 represents a circle with radius 6 then c is