The line which is parallel to x - axis and crosses the curve y = at an angle 45°, is
y =
y = 1
y = 4
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
D.
touch each other externally
Given equation of circles are,
x2 + y2 + 6x + 6y = 0 ...(i)
x2 + y2 - 12x - 12y = 0 ...(ii)
Here, g1 = 3, f1 = 3, g2 = - 6 and f2 = - 6
Centres of circles are C1(- 3,- 3) and C2(6, 6) respectively and radii are r1 = and r2 = respectively.
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 equation of the ellipse having vertices at (± 5, 0) and foci (± 4, 0) is
9x2 + 25y2 = 225
4x2 + 5y2 = 20