Statement 1 : The center of the circle having `x+y=3` and `x-y=1` as its normals is (1, 2) Statement 2 : The normals to the circle always pass through its center

Statement 1 : Any chord of the conic x^2+y^2+x y=1 through (0, 0) is bisected at (0, 0). Statement 2 : The center of a conic is a point through which every chord is bisected.

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

Find the center of the circle x=-1+2costheta,y=3+2sintheta .

Find the center of circle (x+2)^2+(y+4)^2=16

Statement 1: The line x-y-5=0 cannot be normal to the parabola (5x-15)^2+(5y+10)^2=(3x-4y+2)^2dot Statement 2: Normal to parabola never passes through its focus.

Statement 1 : Let S_1: x^2+y^2-10 x-12 y-39=0, S_2 x^2+y^2-2x-4y+1=0 and S_3:2x^2+2y^2-20 x=24 y+78=0. The radical center of these circles taken pairwise is (-2,-3)dot Statement 2 : The point of intersection of three radical axes of three circles taken in pairs is known as the radical center.

The radius of the circle passing through (6,2) and the equation of two normals for the circle are x+y=6 and x+2y=4 is

Statement 1 : The locus of the center of a variable circle touching two circle (x-1)^2+(y-2)^2=25 and (x-2)^2+(y-1)^2=16 is an ellipse. Statement 2 : If a circle S_2=0 lies completely inside the circle S_1=0 , then the locus of the center of a variable circle S=0 that touches both the circles is an ellipse.

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

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