The locus of center of a circle which passes through the origin and cut off a length of 4 units from the line x = 3 is 1) y2 + 6x = 0 2) y2 + 6x = 13 3) y2 + 6x = 10 4) x2 + 6y = 13 Solution: (2) y2 + 6x = 13... View Article
The equations of the circle which pass through the origin and make intercepts of lengths 4 and 8 on the X and Y – axes respectively, are 1) x2 + y2 ± 4x ± 8y = 0 2) x2 + y2 ± 2x ± 4y = 0 3) x2 + y2 ± 8x ± 16y = 0 4) x2 + y2 ± x ± y = 0 Solution: (1) x2 + y2 ± 4x ± 8y = 0... View Article
The area (in sq units) of the circle which touches the lines 4x + 3y = 15 and 4x + 3y = 5 is 1) 4π 2) 3π 3) 2π 4) π Solution: (4) π... View Article
The equation of a circle which touches the lines x = y at origin and passes through the point (2, 1) is x2 + y2 + px + qy = 0. Then, p, q are 1) -5, 5 2) -5, 5 3) 5, - 5 4) None of these Solution: (2) -5, 5 Let the equation of the circle passing through origin be x2 + y2... View Article
The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 sq. units. Then the equation of this circle is 1) x2 + y2 + 2x – 2y = 62 2) x2 + y2 + 2x – 2y = 47 3) x2 + y2 – 2x + 2y = 47 4) x2 + y2 – 2x + 2y = 62 Solution: (3) x2 + y2 – 2x + 2y = 47... View Article
The coordinates of the centre of the smallest circle passing through the origin and having y = x + 1 as a diameter, are 1) (1/2, - (1/2)) 2) (1/2, 1/3) 3) (-1, 0) 4) (-(1/2), 1/2) Solution: (4) (-(1/2), 1/2) Let equation of the line perpendicular to... View Article
If the two circles (x – 1)2 + (y – 3)2 = r2 and x2 + y2 – 8x + 2y + 8 = 0 intersect in two distinct points, then 1) 2 < r < 8 2) r < 2 3) r = 2 4) r > 2 Solution: (1) 2 < r < 8... View Article
If a circle passes through (0, 0), (a, 0) and (0, b), then the coordinates of its centre are 1) (b/2, a/2) 2) (a/2, b/2) 3) (b, a) 4) (a, b) Solution: (2) (a/2, b/2) The equation of a circle having centre (h, k), having... View Article
The distance of the midpoint of the line joining two points (4, 0) and (0, 4) from the centre of the circle x2 + y2 = 16 is 1) √2 2) 2√2 3) 3√2 4) 2√3 Solution: (2) 2√2... View Article
The line segment joining points (4, 7) and (-2, -1) are the diameter of a circle. If the circle intersects the X-axis at A and B, then AB is equal to 1) 4 2) 5 3) 6 4) 8 Solution: (4) 8 The equation of circle is (x - 4)(x + 2) + (y -7)(y + 1) = 0 If the circle cut the x axis... View Article
The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x – 4y = m at two distinct points, if 1) -85 < m < - 35 2) -35 < m < 15 3) 15 < m < 65 4) 35 < m < 85 Solution: (2) -35 < m < 15... View Article
The intercept on the line y = x by the circle x2 + y2 – 2x = 0 is AB. Equation of the circle with AB as diameter is 1) x2 + y2 = 1 2) x(x - 1) + y(y - 1) = 0 3) x2 + y2 = 2 4) (x - 1) (x - 2) + (y - 1) (y - 2) = 0 Solution: (2) x(x - 1) + y(y - 1) = 0... View Article
The locus of the midpoint of a chord of the circle x2 + y2 = 4 which subtends a right angle at the origin is 1) x + y = 2 2) x2 + y2 = 1 3) x2 + y2 = 2 4) x + y = 1 Solution: (3) x2 + y2 = 2... View Article
The circle passing through the point(-1, 0) and touching the Y – axis at (0, 2), also passes through the point 1) (-(3/2), 0) 2) (-(5/2), 2) 3) (-(3/2), 5/2) 4) (-4, 0) Solution: (4) (-4, 0) Circle touching y-axis at (0, 2) is (x - 0)2 + (y... View Article
The equation of the circle passing through (1, 1) and the points of intersection of x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0 is 1) 4x2 + 4y2 - 30x - 10y - 25 = 0 2) 4x2 + 4y2 + 30x - 13y - 25 = 0 3) 4x2 + 4y2 - 17x - 10y + 25 = 0 4) none of these Solution: (2) 4x2 +... View Article
The least and the greatest distance of the point (10, 7) from the circle x2 + y2 – 4x – 2y – 20 = 0 are 1) 10, 5 2) 15, 20 3) 12, 16 4) 5, 15 Solution: (4) 5, 15... View Article
If the equation of the tangent to the circle x2 + y2 – 2x + 6y – 6 = 0 parallel to 3x – 4y + 7 = 0 is 3x – 4y + k = 0, then the values of k are 1) 5, -35 2) -5, 35 3) 7, - 32 4) -7, 32 5) None of these Solution: (1) 5, -35... View Article
The circle passing through (1, – 2) and touching the X-axis at (3, 0), also passes through the point 1) (-5, 2) 2) (2, -5) 3) (5, - 2) 4) (-2, 5) Solution: (3) (5, - 2)... View Article
The centre of the circle passing through the point (0, 1) and touching the curve y = x2 at (2, 4) is 1) [- 16 / 5, 27 / 10] 2) [- 16 / 7, 53 / 10] 3) [- 16 / 5, 53 / 10] 4) None of these Solution: (3) [- 16 / 5, 53 / 10]... View Article
Compute the shortest distance between the circle x2 + y2 – 10x – 14y – 151 = 0 and the point (-7, 2). 1) 0 2) 1 3) 2 4) 4 Solution: (3) 2... View Article
