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` (A) Both the statement are True and Statement 2 is the correct explanation of Statement 1. (B) Both the statement are True but Statement 2 is not the correct explanation of Statement 1. (C) Statement 1 is True and Statement 2 is False. (D) Statement 1 is False and Statement 2 is True.

Statement-1: A circle can be inscribed in a quadrilateral whose sides are 3x -4y =0, 3x -4y= 5, 3x+ 4y= 0 and 3x+ 4y= 7 Statement-2: A circle can be inscribed in a parallelogram if and only if it is a rhombus (a) statement-1 is true, statement-2 is true and statement-2 is correct explanation for Statement-1. (b) Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1. (c) Statement-1 is true, statement-2 is false. d) Statement-1 is false, statement-2 is true

The equation of the diameter of the circle x^2 + y^2 + 4x + 4y-11=0 , which bisects the chord cut off by the circle on the line 2x-3y-3=0 is 3x+2y+10=0 . Statement 2 : The diameter of a circle is a chord of the circle of maximum length. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

x-y+b=0 is a chord of the circle x^2 + y^2 = a^2 subtending an angle 60^0 in the major segment of the circle. Statement 1 : b/a = +- sqrt(2) . Statement 2 : The angle subtended by a chord of a circle at the centre is twice the angle subtended by it at any point on the circumference. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement 1 : The circle x^2 + y^2 - 8x - 6y + 16=0 touches x-axis. Statement : 2 : y-coordinate of the centre of the circle x^2 + y^2 - 8x -6y+16=0 is numerically equal to its radius. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

The line L_1:""y""-""x""=""0 and L_2:""2x""+""y""=""0 intersect the line L_3:""y""+""2""=""0 at P and Q respectively. The bisector of the acute angle between L_1 and L_2 intersects L_3 at R. Statement-1 : The ratio P R"":""R Q equals 2sqrt(2):""sqrt(5) Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles. Statement-1 is true, Statement-2 is true ; Statement-2 is correct explanation for Statement-1 Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statement-1 Statement-1 is true, Statement-2 is false Statement-1 is false, 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.

Assertion: The lines x/1=y/2=z/3 and (x-1)/(-2)=(y-2)/(-4)=(z-3)/(-6) are parallel., Reason: two lines having direction ratios l_1,m_1,n_1 and l_2,m_2,n_2 are parallel if l_1/l_2=m_1/m_2=n_1/n_2 . (A) Both A and R are true and R is the correct explanation of A (B) Both A and R are true R is not the correct explanation of A (C) A is true but R is false. (D) A is false but R is true.

Statement I The line 3x-4y=7 is a diameter of the circle x^(2)+y^(2)-2x+2y-47=0 Statement II Normal of a circle always pass through centre of circle

If one of the diameters of the circle x^2+y^2-2x-6y+ 6 = 0 is a chord to the circle with centre (2, 1), then the radius of circle is:

Statement-1: The lines y=mx+1-m for all values of m is a normal to the circle x^(2)+y^(2)-2x-2y=0 . Statement-2: The line L passes through the centre of the circle.