Related InterviewSolutions

• Consider the circles S1 : x2 + y2 + 2x + 4y + 1 = 0 S2 : x2 + y2 – 4x + 3 = 0 S3 : x2 + y2 + 6y + 5 = 0 Which of this following statements are correct? (A) Radical centre of S1, S2 and S3 lies in 1st quadrant. (B) Radical centre of S1, S2 and S3 lies in 4th quadrants. (C) Radius of the circle intersecting S1, S2 and S3 orthogonally is 1. (D) Circle orthogonal to S1, S2 and S3 has its x and y intercept equal to zero.
• Given the family of lines, a (3x + 4y + 6) + b (x + y + 2) = 0 . The line of the family situated at the greatest distance from the point P (2, 3) has equation :(A) 4x + 3y + 8 = 0 (B) 5x + 3y + 10 = 0 (C) 15x + 8y + 30 = 0 (D) none
• A and B are two fixed points whose co-ordinates are (3, 2) and (5, 4) respectively. The co-ordinates  of a point P if ABP is an equilateral triangle, is/are :(A) (-4√3 , 3+ √3)(B) (4+ √3 , 3- √3)(C) (3-√3 , 4+√3)(D) (3+ √3 , 4-√3)
• The straight lines x + y = 0, 3x + y - 4 = 0 and x + 3y - 4 = 0 form a triangle which is (A) isosceles (B) right angled (C) obtuse angled (D) equilateral
• The locus of the centers of the circles which cut the circles x2 + y2 + 4x - 6y + 9 = 0 and x2 + y2 - 5x + 4y - 2 = 0 orthogonally is : (A) 9x + 10y - 7 = 0 (B) x - y + 2 = 0 (C) 9x - 10y + 11 = 0 (D) 9x + 10y + 7 = 0
• Straight lines 2x + y = 5 and x - 2y = 3 intersect at the point A . Points B and C are chosen on these two lines such that AB = AC . Then the equation of a line BC passing through the point (2, 3) is (A) 3x - y - 3 = 0 (B) x + 3y - 11 = 0 (C) 3x + y - 9 = 0 (D) x - 3y + 7 = 0
• Column-IColumn-II(A) Two intersecting circles(P) have a common tangent(B) Two circles touching each other(Q) have a common normal(C) Two non-concentric circles, one strictly inside  the other(R) do not have a common normal(D) Two concentric circles of different radii(S) do not have a radical axis.
• The locus of the middle points of the system of chords of the circle x2 + y2 = 16 which are parallel to the line 2y = 4x + 5 is (A) x = 2y (B) x + 2y = 0 (C) y + 2x = 0 (4) y = 2x
• Determine the position of the points (2, 1) and (-1, 1) w.r.t the line 4x – ly + 1 = 0. 
• The points (x1, y1) , (x2, y2) , (x1, y2) and (x2, y1) are always : (A) collinear (B) concyclic (C) vertices of a square (D) vertices of a rhombus