The locus of the vertices of the family of parabolas y = [a3x2 / 3] + (a2x / 2) – 2a is
1) xy = 3/4 2) xy = 35/16 3) xy = 64/105 4) xy = 105/64 Solution: (4) xy =... View Article
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Axis of a parabola is y = x and vertex and focus are at a distance √2 and 2√2, respectively from the origin. Then, equation of the parabola is
1) (x – y)2 = 8 (x + y – 2) 2) (x + y)2 = 2 (x + y... View Article
If e1 is the eccentricity of the ellipse (x2 / 16) + (y2 / 25) = 1 and e2 is the eccentricity of the hyperbola passing through the foci of the ellipse and e1e2 = 1, then the equation of the hyperbola is
1) (x2 / 9) – (y2 / 16) = 1 2)(x2 / 16) – (y2 / 9) = – 1... View Article
If P be the point (1, 0) and Q a point on the locus of y2 = 8x. The locus of mid – point of PQ is
1) x2 – 4y + 2 = 0 2) x2 + 4y + 2 = 0 3) y2 – 4x... View Article
The lines x = at2 meets the ellipse (x2 / a2) + (y2 / b2) = 1, in the real points, iff
1) |t|< 2 2) |t| ≤ 1 3) |t|> 1 4) None of these Solution: (2) |t| ≤ 1 (x2... View Article
The curve represented by x = 3 (cos t + sin t) and y = 4(cos t – sin t) is
1) an ellipse 2) a parabola 3) a hyperbola 4) a circle Solution: (1) an ellipse x = 3(cos t... View Article
The parametric representation of a point of the ellipse whose foci are (- 3, 0) and (9, 0) and eccentricity 1/3 is
1) (3 + 8 cos θ, 12 √2 sin θ) 2) (1 + 3 cos θ, 5 sin θ) 3)... View Article
If (x2 / 36) – (y2 / k2) = 1 is a hyperbola, then which of the following statements can be correct?
1) (-3. 1) lies on the hyperbola 2) (3, 1) lies on the hyperbola 3) (10, 4) lies on the... View Article
The equation of an ellipse whose eccentricity is 1/ 2 and the vertices are (4, 0) and (10, 0), is
1) 3x2 + 4y2 – 42x + 120 = 0 2) 3x2 + 4y2 + 42x + 120 = 0... View Article
The parametric representation of a point on the ellipse whose foci are ( -1, 0) and (7, 0) and eccentricity 1/2 is
1) (3 + 8 cos θ, 4 √3 sinθ) 2) ( 8 cos θ, 4 √3 sinθ) 3) (3 +... View Article
The curve described para metrically by x = t2 + 2t – 1, y = 3t + 5 represents
1) an ellipse 2) a hyperbola 3) a parabola 4) a circle Solution: (3) a parabola Given x = t2... View Article
Equation of the parabola with its vertex at (1, 1) and focus (3, 1) is
1) (x -1)2 = 8 (y – 1) 2) (y -1)2 = 8 (x – 3) 3) (y -1)2 =... View Article
A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x2 + y2 = 12 then, its equation is
1) x2 cosec2 θ – y2 sec2 θ = 1 2) x2 sec2 θ – y2 cosec2 θ = 1... View Article
If O is the origin and A is a point on the curve y2 = 4x. Then, the locus of the mid – point of OA, is
1) x2 = 4y 2) x2 = 2y 3) x2 = 16y 4) y2 = 2x Solution: (4) y2 =... View Article
A point P moves, so that the difference of its distances from (-ae, 0) and (ae, 0) is 2a. Then, the locus of P is
1) (x2 / a2) – (y2 / [a2 (e2 – 1)]) = 1 2) (x2 / a2) + (y2 /... View Article
For an ellipse with eccentricity 1 / 2 the centre is at the origin. If one directrix is x = 4, then the equation of the ellipse is
1) 3x2 + 4y2 = 1 2) 3x2 + 4y2 = 12 3) 4x2 + 3y2 = 1 4) 4x2... View Article
Length of the straight line x – 3y = 1 intercepted by the hyperbola x2 – 4y2 = 1 is
1) (3/5) √10 2) (6/5) √10 3) (5/3) √10 4) (5/6) √10 Solution: 2) (6/5) √10 Given line is x... View Article
The locus of the equation x2 + y2 = 0, is
1) a circle 2) a hyperbola 3) a pair of lines 4) at the origin Solution: (4) at the origin... View Article
If t is a parameter then x = a(t + 1/t) and y = b(t – 1/t) represents
1) an ellipse 2) a circle 3) a pair of straight lines 4) hyperbola Solution: (4) hyperbola x = a(t... View Article
The equation of the ellipse having vertices at (± 5, 0) and foci (± 4, 0) is
1) (x2 / 25) + (y2 / 16) = 1 2) 9x2 + 25y2 = 225 3) (x2 / 9)... View Article
