Let the foci of the ellipse subtend a right angle at a point P. Then, the locus of P is
x2 + y2 = 1
x2 + y2 = 2
x2 + y2 = 4
x2 + y2 = 8
Let P be the mid-point of a chord joining the vertex of the parabola y2 = 8x to another point on it. Then, the locus of P is
y2 = 2x
y2 = 4x
= 1
B.
y2 = 4x
Let the chord be MN.
Let other end of chord joining from vertex to it lying on y = Bx be N (2t2, 4t)
is the required locus of P.
The line x = 2y intersects the ellipse at the points P and Q. The equation of the circle with PQ as diameter is
x2 + y2 = 1
x2 + y2 = 2
x2 + y2 =
The eccentric angle in the first quadrant of a point on the ellipse at a distance units from the centre of the ellipse is
The transverse axis of a hyperbola is along the x - axis and its length is 2a. The vertex of the hyperbola bisects the line segment joining the centre and the focus. The equation of the hyperbola is
6x2 - y2 = 3a2
x2 - 3y2 = 3a2
x2 - 6y2 = 3a2
3x2 - y2 = 3a2
A point moves in such a way that the difference of its distance from two points (8, 0) and (- 8, 0) always remains 4. Then, the locus of the point is
a circle
a parabola
an ellipse
a hyperbola
The incentre of an equilateral triangle is (1, 1) and the equation of one side is 3x + 4y + 3 = 0. Then, the equation of the circumcircle of the triangle is
x2 + y2 - 2x - 2y - 2 = 0
x2 + y2 - 2x - 2y - 14 = 0
x2 + y2 - 2x - 2y + 2 = 0
x2 + y2 - 2x - 2y + 14 = 0
The length of the latus rectum of the ellipse 16x2 + 25y2 = 400 is
5/16 unit
32/5 unit
16/5 unit
5/32 unit