The two parabolas x2 = 4y and y2 = 4x meet in two distinct points. One of these is the origin and the other is
1) (2, 2) 2) (4, -4) 3) (4, 4) 4) (-2, 2) Solution: (3) (4, 4) x2 = 4y and... View Article
Latest Posts
The locus of the mid – point of the line joining focus and any point on the parabola y2 = 4ax is a parabola with the equation of directrix as
1) x + a = 0 2) 2x + a = 0 3) x = 0 4) x = a... View Article
The equation (x2 / (2 – λ)) – y2 / (λ – 5) – 1 = 0 represents an ellipse, if
1) λ > 5 2) λ < 2 3) 2 < λ < 5 4) 2 > λ > 5... View Article
The equation of the parabola whose focus is (3, – 4) and directrix 6x – 7y + 5 = 0, is
1) (7x + 6y)2 – 570x + 750y + 2100 = 0 2) (7x + 6y)2 + 570x – 750y... View Article
x = 4 (1 + cos θ) and y = 3 (1 + sinθ) are the parametric equations of
1) [(x – 3)2 / 9] + [(y – 4)2 / 16] = 1 2) [(x + 4)2 / 16]... View Article
Locus of the point which divides double ordinate of the ellipse (x2 / a2) + (y2 / b2) = 1 in the ratio 1 : 2 internally is
1) (x2 / a2) – (9y2 / b2) = 1 / 9 2) (x2 / a2) + (9y2 / b2)... View Article
A parabola is drawn with its focus at (3, 4) and vertex at the focus of the parabola y2 – 12x – 4y + 4 = 0. The equation of the parabola is
1) y2 – 8x – 6y + 25 = 0 2) y2 – 6x + 8y – 25 = 0... View Article
The equation of the ellipse whose distance between the foci is equal to 8 and distance between the directrix is 18, is
1) 5x2 – 9y2 = 180 2) 9x2 + 5y2 = 180 3) x2 + 9y2 = 180 4) 5x2... View Article
Consider the two curves C1 : y2 = 4x and C2 : x2 + y2 – 6x + 1 = 0, then
1) C1 and C2 touch each other at only one point 2) C1 and C2 touch each other at exactly... View Article
The circle x2 + y2 = a2 intersects the hyperbola xy = c2 in four points (xi, yi), for i = 1, 2, 3 and 4, then y1 + y2 + y3 + y4 equals
1) 0 2) c 3) a 4) c4 Solution: (1) 0 x2 + y2 = a2 — (1) and xy... View Article
Focus of hyperbola is (± 3, 0) and equation of tangent is 2x + y – 4 = 0, find the equation of hyperbola is
1) 4x2 – 5y2 = 20 2) 5x2 – 4y2 = 20 3) 4x2 – 5y2 = 1 4) 5x2... View Article
The ellipse x2 + 4y2 = 4 is inscribed in a rectangle aligned with the coordinate axes, which is turn in inscribed in another ellipse that passes through the point (4, 0). Then, the equation of the ellipse is
1) x2 + 12y2 = 16 2) 4x2 + 48y2 = 48 3) 4x2 + 64y2 = 48 4) x2... View Article
The circle x2 + y2 – 8x = 0 and hyperbola x2/ 9 – y2 / 4 = 1 intersect at the points A and B. Equation of the circle with AB as its diameter is
1) x2 + y2 – 12x + 24 = 0 2) x2 + y2 + 12x + 24 = 0... View Article
The circle x2 + y2 – 8x = 0 and hyperbola x2 / 9 – y2 / 4 = 1 intersect at the points A and B. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is
1) 2x – √5y – 20 = 0 2) 2x – √5y + 4 = 0 3) 3x – 4y... View Article
The parabola y2 = 4x and the circle x2 + y2 – 6x + 1 = 0 will
1) intersect at exactly one point 2) touch each other at two distinct points 3) touch each other at exactly... View Article
The distance between the vertex of the parabola y = x2 – 4x + 3 and the centre of the circle x2 = 9 – (y – 3)2 is
1) 2√3 units 2) 3√2 units 3) 2√2 units 4) √2 units 5) 2√5 units Solution: (5) 2√5 units y... View Article
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3, 1) and has eccentricity √(2 / 5) is
1) 5x2 + 3y2 – 48 = 0 2) 3x2 + 5y2 – 15 = 0 3) 5x2 + 3y2... View Article
If the eccentricity of the hyperbola x2 / a2 – y2 / b2 = 1 is reciprocal to that of the ellipse x2 + 4y2 = 4. If the hyperbola passes through the focus of the ellipse, then
1) the equation of the hyperbola is x2 / 3 – y2 / 2 = 1 2) a focus of... View Article
Let P and Q are the points on the parabola y2 = 4x, if so that the line segment PQ subtends a right angle at the vertex. If PQ intersects the axis of the parabola at R, then the distance of the vertex from R is
1) 1 2) 2 3) 4 4) 6 Solution: (3) 4 (t12, 2t2) and (t22, 2t2) respectively and let the... View Article
If the foci of the ellipse x2 / 9 + y2 = 1 subtend right angle at a point P. Then, the locus of P is
1) x2 + y2 = 1 2) x2 + y2 = 2 3) x2 + y2 = 4 4) x2... View Article
