A circle having centre at the origin passes through the three vertices of an equilateral triangle the length of its median being 9 units. Then the equation of that circle is
A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola at the point (x1, y1). Then is equal to :
10
5
8
6
The number of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2 – 2x – 4y + 4 = 0 at two distinct points is ....
For some , if the eccentricity of the hyperbola, is 5 times the eccentricity of the ellipse , , then the length of the latus rectum of the ellipse, is
C.
The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the vertex of this parabola is
Let e1 and e2 be the eccentricities of the ellipse, respectively satisfying e1e2 = 1. If are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair is equal to:
(8, 10)
(8, 12)
If the tangent to the curve, y = ex at a point (c, ec) and the normal to the parabola, y2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is.....
Let P(3, 3) be a point on the hyperbola, . If the normal to it at P intersects the x-axis at (9,0) and e is its eccentricity, then the ordered pair (a2, e2) is equal to :
Let be agiven ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function then a2 + b2 is equal to
145
126
116
135