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
The equation of circle with centre (- a, – b) and radius √a2 – b2 is Circles and System of Circles 1) x2 + y2 + 2ax + 2by + 2b2 = 0 2) x2 + y2 - 2ax - 2by - 2b2 = 0 3) x2 + y2 - 2ax - 2by + 2b2 = 0 4) x2 + y2... View Article
The general solution of the differential equation dy / dx = cot x cot y is 1) cos x = c cosec y 2) sin x = c sec y 3) sin x = c cos y 4) cos x = c sin y Solution: (2) sin x = c sec y... View Article
The solution of the dy / dx = 1 / x is 1) y + log x + c = 0 2) y = log x + c 3) ylogx + c = 0 4) None of these Solution: (2) y = log x + c dy / dx = 1 / x y = log x + c... View Article
The solution of the differential equation (dy / dx) + sin2 y = 0 is 1) y + 2 cos y = c 2) y - 2 sin y = c 3) x = cot y + c 4) y = cot x + c Solution: (3) x = cot y + c... View Article
The differential equation for the line y = mx + c is (where c is arbitrary constant) 1) (dy / dx) = m 2) (dy / dx) + m = 0 3) dy / dx = 0 4) None of these Solution: (1) (dy / dx) = m y = mx + c dy / dx = m... View Article
The differential equation of all conics whose centre lie at the origin is of order 1) 2 2) 3 3) 4 4) None of these Solution: (2) 3 Equation of all conics: ax2 + 2hxy + by2 = 1, --- a, h, b are arbitrary constants.... View Article
The order of differential equations of all parabolas having directrix parallel to the x-axis is 1) 3 2) 1 3) 4 4) 2 Solution: (1) 3 The equation of all parabolas having directrices parallel to the x-axis is (x - h)2 = ± 4a (y... View Article