The equation of the circle which passes through the points of intersection of the circles x2 + y2 - 6x = 0 and x2 + y2 - 6y = 0 and has its centre at , is
x2 + y2 + 3x + 3y + 9 = 0
x2 + y2 + 3x + 3y = 0
x2 + y2 - 3x - 3y = 0
x2 + y2 - 3x - 3y + 9 = 0
If 2y = x and 3y + 4x = 0 are the equations of a pair of conjugate diameters of an ellipse, then the eccentricity of the ellipse is
If t is a parameter, then x = , y = represents
an ellipse
a circle
a pair of straight lines
a hyperbola
The equation (x - x1)(x - x2) + (y - y1)(y - y2) = 0 represents a circle whose centre is
(x1, y1)
(x2, y2)
The circles x2 + y2 + 6x + 6y = 0 and x2 + y2 - 12x - 12y = 0
cut orthogonally
touch each other internally
intersect in two points
touch each other externally
The two parabolas x2 = 4y and y2 = 4x meet in two distinct points. One of these is the origin and the other is
(2, 2)
(4, - 4)
(4, 4)
(- 2, 2)
If P(at2, 2at) be one end of a focal chord of the parabola y2 = 4ax, then the length of the chord is
a
a
a
a
The length of the common chord of the parabolas y2 = x and x2 = y is
1
C.
The equations of given parabola are,
y2 = x ...(i)
and x2 = y ...(ii)
On solving Eqs. (i) and (ii), we get
x = 0, 1
and y = 0, 1
Points of intersection are (0, 0) and (1, 1).
Hence, length of common chord =
The equation of the ellipse having vertices at (± 5, 0) and foci (± 4, 0) is
9x2 + 25y2 = 225
4x2 + 5y2 = 20