If the line y cos α = xsin α + a cos α is a tangent to the circle x2 + y2 = a2, then 1) sin2 α = 1 2) cos2 α = 1 3) sin2 α = a2 4) cos2 α = a2 Solution: (2) cos2 α = 1... View Article
The angle between the tangents drawn at the points (5, 12) and (12, – 5) to the circles x2 + y2 = 169 is 1) 45o 2) 60o 3) 30o 4) 90o Solution: (4) 90o x2 + y2 = 169 Differentiating w.r.t x 2x + 2y (dy / dx) = 0 dy / dx = − x / y... View Article
Locus of the point of intersection of perpendicular tangents to the circle x2 + y2 = 16 is 1) x2 + y2 = 8 2) x2 + y2 = 32 3) x2 + y2 = 64 4) x2 + y2 = 16 Solution: (2) x2 + y2 = 32 If two perpendicular tangents to the... View Article
The equation of the tangent from the point (0, 1) to the circle x2 + y2 – 2x – 6y + 6 = 0, is 1) 3 (x2 − y2) + 4xy − 4x − 6y + 3 = 0 2) 3y2 + 4xy − 4x − 6y + 3 = 0 3) 3x2 + 4xy − 4x − 6y + 3 = 0 4) 3 (x2 + y2) + 4xy − 4x − 6y + 3 = 0... View Article
The equation of normal of x2 + y2 – 2x + 4y – 5 = 0 at (2, 1) is 1) y = 3x - 5 2) 2y = 3x - 4 3) y = 3x + 4 4) y = x + 1 Solution: (1) y = 3x - 5... View Article
The length (in units) of tangent from point (5, 1) to the circle x2 + y2 + 6x – 4y – 3 = 0 is 1) 81 2) 29 3) 7 4) 21 Solution: (3) 7... View Article
The equation of the two tangents from (- 5, – 4) to the circle x2 + y2 + 4x + 6y + 8 = 0 are 1) x + 2y + 13 = 0, 2x - y + 6 = 0 2) 2x + y + 13 = 0, x - 2y = 6 3) 3x + 2y + 23 = 0, 2x - 3y + 4 = 0 4) x - 7y = 23, 6x + 13y = 4... View Article
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
