The circles x2 + y2 + 4x – 4y + 4 = 0 touches 1) X - axis 2) Y - axis 3) X - axis and Y - axis 4) None of these Solution: (3) X-axis and Y-axis The centre is (−2, 2) and the... View Article
A point P moves in such a way that the ratio of its distance from two coplanar points is always a fixed number (≠1). Then, its locus is a 1) parabola 2) circle 3) hyperbola 4) pair of straight lines Solution: (2) circle... View Article
Which of the following equations given circle? 1) r = 2 sin θ 2) r2 cos 2θ = 1 3) r( 4 cos θ + 5 sin θ) = 3 4) 5 = r (1 + √2 cos θ) Solution: (1) r = 2 sin θ x = r cos θ, y = r... View Article
The locus of the centre of the circle for which one end of a diameter is (1, 1) while the other end is in the line x + y = 3 is 1) x+ y = 1 2) 2(x - y) = 5 3) 2x + 2y = 5 4) None of these Solution: (3) 2x + 2y = 5 Let the centre of the circle be C (h, k) and... View Article
The radius of the circle x2 + y2 + 4x + 6y + 13 = 0 is 1) √26 2) √13 3) √23 4) 0 Solution: (4) 0 x2 + y2 + 4x + 6y + 13 = 0 (x2 + 4x + 4) + (y2 + 6y + 9) + 13 = 4 + 9 (x + 2)2 (y +... View Article
The radius of any circle touching the lines 3x – 4y + 5 = 0 and 6x – 8y – 9 = 0 is 1) 1.9 2) 0.95 3) 2.9 4) 1.45 Solution: (2) 0.95... View Article
Find the equation of the circle passing through the origin and the points where the line 3x + 4y = 12 meets the axes of coordinates. 1) x2 + y2 + 3x + 4y = 0 2) x2 + y2 + 3x - 4y = 0 3) x2 + y2 - 3x + 4y = 0 4) x2 + y2 - 4x - 3y = 0 Solution: (4) x2 + y2 - 4x - 3y =... View Article
If 2x – 4y = 9 and 6x – 12y + 7 = 0 are common tangents to the circle, then radius of circle is 1) √3/5 2) 17/6√5 3) √2/3 4) 17/3√5 Solution: (2) 17/6√5... View Article
The center of the circle x = 2 + 3 cos θ, y = 3 sin θ – 1 is 1) (3, 3) 2) (2, - 1) 3) (-2, 1) 4) (1, - 2) Solution: (2) (2, - 1) x = 2 + 3 cos θ, y = 3 sin θ − 1 or cos θ = (x − 2) / 3, sin θ... View Article
The circle x2 + y2 – 8x + 4y + 4 = 0 touches 1) X - axis 2) Y - axis 3) both axes 4) neither X - axis nor Y - axis Solution: (2) Y-axis x2 + y2 - 8x + 4y + 4 = 0 (x2 - 8x +... View Article
The equation of circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5, is 1) 6 (x2 + y2) + 5 (3x - 2y) = 0 2) x2 + y2 - 2x - 3y + 5 = 0 3) x2 + y2 + 2x - 3y - 5 = 0 4) 6 (x2 + y2) - 5(3x + 2y) = 0 Solution: (4) 6... View Article
The equation of the circle passing through (4, 5) and having the center (2, 2) is 1) x2 + y2 + 4x + 4y - 5 = 0 2) x2 + y2 - 4x - 4y - 5 = 0 3) x2 + y2 - 4x = 13 4) x2 + y2 - 4x - 4y + 5 = 0 Solution: (2) x2 + y2 -... View Article
Suppose a circle passes through (2, 2) and (9, 9) and touches the X-axis at P. If O is the origin, then OP is equal to 1) 4 2) 5 3) 6 4) 9 5) 11 Solution: (3) 6... View Article
The equation of the circle with center (2, 1) and touching the line 3x + 4y = 5 is 1) x2 + y2 - 4x - 2y + 5 = 0 2) x2 + y2 - 4x - 2y - 5 = 0 3) x2 + y2 - 4x - 2y + 4 = 0 4) x2 + y2 - 4x - 2y - 4 = 0 Solution: (3) x2... View Article
One of the diameter of the circle x2 + y2 – 12x + 4y + 6 = 0 is given by 1) x + y = 0 2) x + 3y = 0 3) x = y 4) 3x + 2y = 0 Solution: (2) x + 3y = 0 Given the equation of circle is x2 + y2 - 12x + 4y + 6... View Article
The other end of the diameter through the point (-1, 1) on the circle x2 + y2 – 6x + 4y – 12 = 0 is 1) (-7, 5) 2) (-7, - 5) 3) (7, - 5) 4) (7, 5) Solution: (3) (7, - 5)... View Article
The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0, is 1) x2 + y2 - 6x + 6y + 9 = 0 2) x2 + y2 - 6x - 6y + 9 = 0 3) x2 + y2 + 6x - 6y + 9 = 0 4) x2 + y2 + 6x + 6y + 9 = 0 Solution: (1) x2... View Article
The equation of two circles which touch the Y – axis at (0, 3) and make an intercept of 8 units on X – axis , are 1) x2 + y2 ± 10x - 6y + 9 = 0 2) x2 + y2 ± 6x - 10y + 9 = 0 3) x2 + y2 - 8x ± 10y + 9 = 0 4) x2 + y2 - 10x ± 6y + 9 = 0 Solution: (1)... View Article
A variable circle passes through the fixed point A (p, q) and touches X – axis. The locus of the other end of the diameter through A is 1) (x - p )2 = 4qy 2) (x - q )2 = 4py 3) (y - p )2 = 4qx 4) (y - q )2 = 4px Solution: (1) (x - p )2 = 4qy Since, the coordinates of one end... View Article
The area of the circle centred at (1, 2) and passing through (4, 6) is 1) 5 π sq units 2) 10 π sq units 3) 25 π sq units 4) None of these Solution: (3) 25 π sq units The centre of the circle is C (1,... View Article