The number of feet of normals from the point (7, –4) to the circle x2 + y2 = 5 is 1) 1 2) 2 3) 3 4) 4 Solution: (2) 2... View Article
A foot of the normal from the point (4, 3) to a circle is (2, 1) and a diameter of the circle has the equation 2x – y = 2. Then the equation of the circle is 1) x2 + y2 + 2x – 1 = 0 2) x2 + y2 – 2x – 1 = 0 3) x2 + y2 – 2y – 1 = 0 4) none of these Solution: (2) x2 + y2 – 2x – 1 = 0... View Article
If (2, 4) is a point interior to the circle x2 + y2 – 6x – 10y + λ = 0 and the circle does not cut the axes at any point, then λ belongs to the interval 1) (25, 32) 2) (9, 32) 3) (32, + ∞) 4) None of these Solution: (1) (25, 32)... View Article
Let f(x, y) = 0 be the equation of a circle. If f (0, λ) = 0 has equal roots λ = 2, 2 and f (λ,0) = 0 has roots λ = 4/5, 5, then the centre of the circle is 1) (2, 29 / 10) 2) (29 / 10, 2) 3) (- 2, 29 / 10) 4) none of these Solution: (2) (29 / 10, 2)... View Article
A region in the xy-plane is bounded by the curve x2 + y2 = 25 and the line y = 0. If the point (p, p +1) lies in term of the region, then 1) p ∈ (–1, 3) 2) p ∈ (– ∞, – 1) ∪ (3, ∞) 3) p ∈ (– 4, 3) 4) p ∈ (– ∞, – 1) Solution: (1) p ∈ (–1, 3)... View Article
A line meets the co-ordinate axes an A and B. A circle is circumscribed about the ∆ ABO. If p and q are the distances of the tangents to the circle at the origin from points A and B respectively, then the diameter of the circle is 1) q (p + q) 2) p + q 3) p (p + q) 4) p (p – q) Solution: (2) p + q... View Article
The equation of the circumcircle of an equilateral triangle is x2 + y2 + 2gx + 2fy + c = 0 and one vertex of the triangle is (1, 1). The equation of incircle of the triangle is 1) 4 (x2 + y2) = g2 + f2 2) 4 (x2 + y2) + 8gx + 8fy = (1 – g) (1 + 3g) + (1 – f) (1 + 3f) 3) 4 (x2 + y2) + 8gx + 8fy = g2 + f2 4) none of... View Article
If p and q be the longest distance and the shortest distance respectively of the point (–7, 2) from any point (α, β) on the curve whose equation is x2 + y2 – 10x – 14y – 51 = 0, then G.M. of p and q is equal to 1) 2√11 2) 5√5 3) 13 4) None of these Solution: (1) 2√11... View Article
Two circles, each of radius 5, have a common tangent at (1,1) whose equation is 3x + 4y – 7 = 0 Then their centres are 1) (4, –5), (–2, 3) 2) (4, –3), (–2, 5) 3) (4, 5), (–2, –3) 4) None of these Solution: (3) (4, 5), (–2, –3)... View Article
If the centroid of an equilateral triangle is (1, 1) and its one vertex is (-1, 2), then the equation of its circumcircle is 1) x2 + y2 – 2x – 2y – 3 = 0 2) x2 + y2 + 2x – 2y – 3 = 0 3) x2 + y2 + 2x + 2y – 3 = 0 4) none of these Solution: (1) x2 + y2 – 2x – 2y – 3 =... View Article
A triangle is formed by the lines whose combined equation is given by (x + y – 4)(xy – 2x – y + 2) = 0. The equation of its circumcircle is 1) x2 + y2 – 5x – 3y + 8 = 0 2) x2 + y2 – 3x – 5y + 8 = 0 3) x2 + y2 – 3x – 5y – 8 = 0 4) none of these Solution: (2) x2 + y2 – 3x – 5y + 8 =... View Article
A point P moves such that the sum of the square of its distances from the sides of a square of side unity is 9. Then the locus of P is 1) x2 + y2 = 3 2) x2 - y2 = 4 3) x2 + y2 = 2 4) x2 + y2 - x - y - (7 / 2) = 0 Solution: (4) x2 + y2 - x - y - (7 / 2) = 0... View Article
The radius of the circle passing through the point P (6, 2), two of whose diameters are x + y = 6 and x + 2y = 4 is 1) 10 2) 2√5 3) 6 4) 4 Solution: (2) 2√5 x + y = 6 and x + 2y = 4... View Article
The value of λ such that the line joining the origin to the points of intersection of the line x + y = 1 and the curve x2 + y2 + x −2y − λ= 2 0 are mutually perpendicular is 1) 1 / 2 2) 1 / 3 3) 2 4) 3 Solution: (1) 1 / 2... View Article
The number of common tangents of the circles (x + 3)2 + (y – 2))2 = 49 and (x – 2) )2 + (y + 1) )2 = 4 1) 0 2) 1 3) 3 4) 4 Solution: (2) 1... View Article
The shortest distance of the point (6, – 8) from the circle x2 + y2 = 36, is 1) 4 2) 6 3) 8 4) 10 Solution: (1) 4 Centre and radius of the circle x2 + y2 = 36 are (0,0) and 6. The point (6,- 8) is outside... View Article
The locus of the centre of the circle, which cuts the circle x2 + y2 – 20x + 4 = 0 orthogonally and touches the line x = 2, is 1) x2 = 16y 2) y2 = 4x 3) y2 = 16x 4) x2 = 4y Solution: (3) y2 = 16x Let the equation of the required circle be x2 + y2 + 2gx +... View Article
A circle passes through the points (0, 0) and (0, 1) and also touches the circle x2 + y2 = 16. The radius of the circle is 1) 1 2) 2 3) 3 4) 4 5) 5 Solution: (2) 2 Since (0,0) and (0,1) lies inside the circle x2 + y2 = 16, the circle will touch the... View Article
The centre of the circle, whose radius is 5 and which touches the circle x2 + y2 – 2x – 4y – 20 = 0 at (5, 5) is 1) (10, 5) 2) (5, 8) 3) (5, 10) 4) (8, 9) 5) (9, 8) Solution: (5) (9, 8) x2 + y2 - 2x - 4y - 20 = 0 (x - 1)2 + (y - 2)2 = 52 Centre of... View Article
The shortest distance between the circles (x – 1)2 + (y + 2)2 = 1 and (x + 2)2 + (y – 2)2 = 4 is 1) 1 2) 2 3) 3 4) 4 5) 5 Solution: (2) 2... View Article
