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 : The number of circles touching lines x+y=1,2x-y=5, and 3x+5y-1=0 is four Statement 2 : In any triangle, four circles can be drawn touching all the three sides of the triangle. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1 (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1 (c) Statement 1 is true but Statement 2 is false (d) Statement 2 is true but Statement 1 is false

The normal to-be circle x^2 +y^2 - 4x + 6y -12=0 passes through the point

Consider two circles x^2+y^2-4x-6y-8=0 and x^2+y^2-2x-3=0 Statement 1 : Both the circles intersect each other at two distinct points. Statement 2 : The sum of radii of the two circles is greater than the distance between their centers. (a) Statement 1 and Statement 2 , both are correct. Statement 2 is correct explanation for Statement 1. (b) Statement 1 and Statement 2 , both are correct. Statement 2 is not the correct explanation for Statement 1. (c) Statement 1 is correct but Statement 2 is not correct. (d) Statement 2 is correct but Statement 1 is not correct.

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

Statement 1: The circumcircle of a triangle formed by the lines x=0,x+y+1=0 and x-y+1=0 also passes through the point (1, 0). Statement 2: The circumcircle of a triangle formed by three tangents of a parabola passes through its focus. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

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.

Find the equation of the normal to the curve x^(2)=4y, which passes through the point (1,2).

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. (a) Statement 1 and Statement 2 are correct. Statement 2 is the correct explanation for the Statement 1. (b) Statement 1 and Statement 2 are correct. Statement 2 is not the correct explanation for the Statement 1. (c) Statement 1 is true but Statement 2 is false. (d) Statement 2 is true but Statement 1 is false.

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

Find the equation of the normal to the curve x^(2) = 4y which passes through the point (1, 2).