Circles `x^2 + y^2 = 1 and x^2 + y^2 - 8x + 11=0` cut off equal intercepts on a line through the point `(-2, 1/2)`. The slope of the line is : (A) `(-1 + sqrt(29))/14` (B) `1+sqrt(7)/4` (C) `(-1-sqrt(29))/14` (D) none of these

The image of the centre of the circle x^2 + y^2 = 2a^2 with respect to the line x + y = 1 is : (A) (sqrt(2), sqrt(2) (B) (1/sqrt(2) , sqrt(2) ) (C) (sqrt(2), 1/sqrt(2)) (D) none of these

If the slope of a line passing through the points (1,4) and (x,2) is 2 , find the value of x .

The distance between the parallel planes x+2y-3z=2 and 2x+4y-6z+7=0 is (A) 1/sqrt(14) (B) 11/sqrt(56) (C) 7/sqrt(56) (D) none of these

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The value of ("lim")_(xvec2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

A(1/(sqrt(2)),1/(sqrt(2))) is a point on the circle x^2+y^2=1 and B is another point on the circle such that are length A B=pi/2 units. Then, the coordinates of B can be (a) (1/(sqrt(2)),-1/sqrt(2)) (b) (-1/(sqrt(2)),1/sqrt(2)) (c) (-1/(sqrt(2)),-1/(sqrt(2))) (d) none of these

The direction cosines of line joining (1,-1,1) and (-1,1,1) are (A) 2,-2,0 (B) 1,-1,0 (C) 1/sqrt(2)-1/sqrt(2),0 (D) none of these

A square is inscribed in the circle x^2+y^2-2x+4y+3=0 . Its sides are parallel to the coordinate axes. One vertex of the square is (1+sqrt(2),-2) (b) (1-sqrt(2),-2) (1,-2+sqrt(2)) (d) none of these

If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then the tangent of the angle subtended by line segment A B at the origin is (a) (8sqrt(3))/(205) (b) (8sqrt(3))/(209) (c) (8sqrt(3))/(215) (d) none of these