If the eccentricity of a hyperbola is √3, then the eccentricity of its conjugate hyperbola is
1) √2 2) √3 3) √3 / 2 4) 2√3 Solution: (3) √3 / 2 (1 / e2) + (1... View Article
Latest Posts
If b and c are the lengths of the segments of any focal chord of a parabola y2 = 4ax, then the length of the latus rectum is
1) bc / [b + c] 2) √bc 3) [b + c] / 2 4) [2bc / (b + c)]... View Article
For the ellipse 25x2 + 9y2 – 150x – 90y + 225 = 0, the eccentricity is equal to
1) 2/5 2) 3/5 3) √15 / 24 4) 4/5 Solution: (4) ⅘ 25x2 + 9y2 – 150x – 90y... View Article
The area of the quadrilateral formed by the tangents at the endpoints of the latus rectum to the ellipse x2 / 9 + (y2 / 5) = 1, is
1) 27/4 sq. units 2) 9 sq. units 3) 27/2 sq. units 4) 27 sq. units Solution: (4) 27 sq.... View Article
The eccentricity of the conic 4x2 + 16y2 – 24x – 32y = 1 is
1) 1/2 2) √3 3) √3/2 4) √3/4 Solution: (3) √3/2 4x2 + 16y2 – 24x – 32y = 1... View Article
The equation of the common tangent to the curves y2 = 8x and xy = -1 is
1) 3y = 9x + 2 2) y = 2x + 1 3) 2y = x + 8 4) y... View Article
If the eccentricity of the ellipse (x2 / 4) + (y2 / 3) = 1 and the hyperbola (x2 / 64) – (y2 / b2) = 1 are reciprocals of each other, then b2 =
1) 192 2) 64 3) 16 4) 32 5) 128 Solution: (1) 192 (x2 / 4) + (y2 / 3)... View Article
The eccentricity of the hyperbola in the standard form (x2 / a2) + (y2 / b2) = 1, passing through (3, 0) and (3√2, 2) is
1) 13/3 2) √13 3) √3 4) √13/3 5) 5/3 Solution: (4) √13/3 (x2 / a2) + (y2 / b2)... View Article
The locus of the point which moves such that the ratio of its distance from two fixed points in the plane is always a constant K (< 1) is
1) a hyperbola 2) an ellipse 3) a straight line 4) a circle Solution: (2) an ellipse The locus of... View Article
The ellipse (x2 / 25) + (y2 / 16) = 1 and the hyperbola (x2 / 25) – (y2 / 16) = 1 have in common
1) centre only 2) centre, foci and directrices 3) centre, foci and vertices 4) centre and vertices Solution: (4) centre... View Article
The eccentricity of the hyperbola 9x2 – 16y2 – 18x – 64y – 199 = 0 is
1) 16/9 2) 5/4 3) 25/16 4) 0 Solution: (2) 5 / 4 9x2 – 16y2 – 18x – 64y... View Article
The eccentricity of the hyperbola conjugate to x2 – 3y2 = 2x + 8 is
1) 2/√3 2) √3 3) 2 4) None of these Solution: (3) 2 x2 – 3y2 = 2x + 8... View Article
The equation of the directrix of the parabola x2 + 8y – 2x = 7 is
1) y = 3 2) y = -3 3) y = 2 4) y = 0 Solution: (1) y =... View Article
Suppose S and S’ are foci of the ellipse (x2 / 25) + (y2 / 16) = 1. If P is a variable point on the ellipse and △ is the area of the △PSS’ then the maximum value of △ is
1) 8 2) 12 3) 16 4) 20 Solution: (2) 12 (x2 / 25) + (y2 / 16) = 1... View Article
The ends of the latus rectum of the conic x2 + 10x – 16y + 25 = 0 are
1) (3, – 4), (13, 4) 2) (-3, -4), (13, -4) 3) (3, 4), (-13, 4) 4) (5, -8), (-5,... View Article
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix
1) x = -a 2) x = -a/2 3) x = 0 4) x = a/2 Solution: (3) x =... View Article
If a > 2b > 0 then the positive value of m for which y = mx – b √1 + m2 is a common tangent to x2 + y2 = b2 and (x – a)2 + y2 = b2 is
1) 2b / √a2 – 4b2 2) √a2 – 4b2 / 2b 3) 2b / (a – 2b) 4) b... View Article
Coordinates of the foci of the ellipse 5x2 + 9y2 + 10x – 36y – 4 = 0, are
1) (1, 2) and (-3, 2) 2) (2, 1) and (-3, 2) 3) (1, 2) and (3, 2) 4) None... View Article
The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is
1) x = -1 2) x = 1 3) x = -3/2 4) x = 3/2 Solution: (4) x =... View Article
The equation of the common tangent touching the circle (x – 3)2 + y2 = 9 and the parabola y2 = 4x above the x-axis is
1) √3y = 3x + 1 2) √3y = – (x + 3) 3) √3y = x + 3 4)... View Article
