If t1 and t2 are the parameters of the end points of a focal chord for the parabola y2 = 4ax, then which one is correct
1) t1 t2 = 1 2) t1 / t2 = 1 3) t1 t2 = – 1 4) t1 +... View Article
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The eccentricity of the hyperbola with latusrectum 12 and semi – conjugate axis 2√3 is
1) 3 2) √3 / 2 3) 2√3 4) 2 Solution: (4) 2 Latus rectum = 2b2 / a =... View Article
The length of the latusrectum of the ellipse 16x2 + 25y2 = 400 is
1) 5/6 units 2) 32/5 units 3) 16/5 units 4) 5/32 units Solution: (2) 32/5 units 16x2 + 25y2 =... View Article
The sum of the reciprocals of the focal distance of a focal chord PQ of y2 = 4ax is
1) 1/a 2) a 3) 2a 4) 1/2a Solution: (1) 1 / a The latus rectum with ends (a, 2a),... View Article
The straight lines y = ± x intersect the parabola y2 = 8x in points P and Q, then length of PQ is
1) 4 2) 4√2 3) 8 4) 16 Solution: (4) 16 y2 = 8x y2 = ± 8y y (y... View Article
If the centre, one of the foci and semi – major axis of an ellipse are (0, 0), (0, 3) and 5, then its equation is
1) x2 / 16 + y2 / 25 = 1 2) x2 / 25 + y2 / 16 = 1... View Article
If (x, y) are any point on the parabola y2 = 4x. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then, the locus of P is
1) x2 = y 2) y2 = 2xy 3) y2 = x 4) x2 = 2y Solution: (3) y2 =... View Article
The equation y2 + 4x + 4y + k = 0 represents a parabola whose latusrectum is
1) 1 2) 2 3) 3 4) 4 Solution: (4) 4 y2 + 4x + 4y + k = 0... View Article
A hyperbola passes through (3, 3) and the length of its conjugate axis is 8. The length of the latus rectum is
1) 20/3 2) 40/3 3) 50/3 4) None of these Solution: (2) 40/3 2b = 8 b = 4 as... View Article
If the length of the major axis of the ellipse (x2 / a2) + (y2 / b2) = 1 is 3 times the length of the minor axis, its eccentricity is
1) 1/3 2) 1/√3 3) √2 / 3 4) 2√2/3 Solution: (4) 2√2/3 The equation of the ellipse is (x2... View Article
If the equation of parabola is x2 = – 8y, then equation of directrix length of latus rectum are
1) y = – (9/8), 8 2) y = 2, 8 3) y = – (9/4), 9 4) None of... View Article
Each of the four inequalities given below defines a region in the xy plane. One of these 4 regions does not have the following property. For any 2 points (x1, y1) and (x2, y2) in the region, the point [(x1 + x2) / 2, [y1 + y2] / 2] is also in the region. The inequality defining this region is
1) x2 + 2y2 ≤ 1 2) Max {|x| , | y|| ≤ 1 3) x2 – y2 ≤ 1 4)... View Article
On the ellipse 9x2 + 25y2 = 225, then find the point the distance from which to our focus F1 is four times the distance to the other focus F2
1) (-15, √63) 2) (- 15 / 4, √63 / 2) 3) (- 15 / 4, √63 / 4) 4)... View Article
A hyperbola passing through a focus of the ellipse (x2 / 169) + (y2 / 25) = 1. Its transverse axis and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of eccentricities is 1. Then, the equation of the hyperbola is
1) (x2 / 144) – (y2 / 9) = 1 2) (x2 / 169) – (y2 / 25) = 1... View Article
An ellipse passing through (4√2, 2√6) has foci at (-4, 0) and (4, 0). Then, its eccentricity is
1) √2 2) 1/2 3) 1/√2 4) 1/√3 Solution: (2) 1 / 2 Since foci are (- 4, 0) and... View Article
The value of λ for which the curve (7x + 5)2 + (7y + 3)2 = λ2 (4x + 3y – 24)2 represents a parabola is
1) ± (6/5) 2) ± (7/5) 3) ± (1/5) 4) ± (2/5) Solution: (2) ± (7/5) (7x + 5)2 +... View Article
The equation x2 / [1 – r] – y2 / [1 + r] = 1, r > 1 represents
1) an ellipse 2) a hyperbola 3) a circle 4) none of these Solution: (4) none of these [x2 /... View Article
The length of the transverse axis of a hyperbola is 2cos α. The foci of the hyperbola are the same as that of the ellipse 9x2 + 16y2 = 144. The equation of the hyperbola is
1) [x2 / cos2 ɑ] – [y2 / (7 – cos2 ɑ)] = 1 2) [x2 / cos2 ɑ] –... View Article
If the eccentricity of the hyperbola (x2 / a2) – (y2 / b2) = 1 is 5 / 4 and 2x + 3y – 6 = 0 is a focal chord of the hyperbola, then the length of the transverse axis is =
1) 12/5 2) 16 3) 24/7 4) 24/5 5) 12/7 Solution: (4) 24 / 5 The focus of the given... View Article
If the length of the latus rectum and the length of the transverse axis of a hyperbola are 4√3 and 2√3 respectively, then the equation of the hyperbola is
1) (x2 / 3) – (y2 / 4) = 1 2) (x2 / 3) – (y2 / 9) = 1... View Article
