The equation of the circle which touches both the axis and whose radius is a, is
1) x2 + y2 – 2ax – 2ay + a2 = 0 2) x2 + y2 + ax + ay... View Article
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The equation of the smallest circle passing through the intersection of the line x + y =1 and the circle x2 + y2 = 9 is
1) x2 + y2 + x + y – 8 = 0 2) x2 + y2 – x – y... View Article
Lines are drawn to the point P(–2, –3) to meet the circle x2 + y2 – 2x – 10y + 1 = 0. The length of the line segment PA, A being the point on the circle where the line meets the circle at coincident points, is
1) 16 2) 4√3 3) 48 4) None of these Solution: (2) 4√3 \(\begin{array}{l}\mathrm{PA} =\text { length of the tangent... View Article
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 \(\begin{array}{l}\text { Since the point (7,-4) lies outside }... 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... 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) \(\begin{array}{l}\text \... 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... 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,... 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:... 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... 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 \(\begin{array}{l}\begin{array}{l} \text { The centre } \mathrm{C}... 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:... 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... 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... 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... 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... 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 \(\begin{array}{l}\text {Make homogeneous}... 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 \(\begin{array}{l}\text { The given circles have centre at }... 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... 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 =... View Article
