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Statement 1 : The equation x^2+y^2-2x-2a...

Statement 1 : The equation `x^2+y^2-2x-2a y-8=0` represents, for different values of `a ,` a system of circles passing through two fixed points lying on the x-axis. Statement 2 : `S=0` is a circle and `L=0` is a straight line. Then `S+lambdaL=0` represents the family of circles passing through the points of intersection of the circle and the straight line (where `lambda` is an arbitrary parameter).
(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

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Statement 1: There are no common tangents between the circle x^2+y^2-4x+3=0 and the parabola y^2=2xdot Statement 2:Given circle and parabola do not intersect. (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: 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 : The equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0 is x-y=0 Statement 2 : y+x=0 is the common chord of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y-4=0 (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 : If the circle with center P(t ,4-2t),t in R , cut the circles x^2+y^2=16 and x^2+y^2-2x-y-12=0 , then both the intersections are orthogonal. Statement 2 : The length of tangent from P for t in R is the same for both the given circles. (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

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.

Statement 1 : The least and greatest distances of the point P(10 ,7) from the circle x^2+y^2-4x-2y-20=0 are 6 units and 15 units, respectively. Statement 2 : A point (x_1,y_1) lies outside the circle S=x^2+y^2+2gx+2fy+c=0 if S_1>0, where S_1=x_1^2+y_1^2+2gx_1+2fy_1+c (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 differential equation of the family of circles passing through the fixed points (a, 0) and (-a, 0) is

Find the equation of the smallest circle passing through the point of intersection of the line x+y=1 and the circle x^(2)+y^(2)=9 .

Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with the x-axis.

The centre of a circle passing through the points (0,0),(1,0)and touching the circle x^2+y^2=9 is

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  12. Statement : Points (1, 1), (2, 3), and (3, 5) are collinear.

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  13. Statement 1 : The number of circles touching lines x+y=1,2x-y=5, and 3...

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  14. The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the...

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  16. A rhombus is inscribed in the region common to the two circles x^2+y^2...

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