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
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)
C.
(4, 4)
Given equations of parabolas are,
x2 = 4y ...(i)
and y2 = 4x ...(ii)
From Eqs. (i) and (ii), we get
On putting the values of x in Eq. (i), we get
y = 0 and y = 4
Points of intersection are (0, 0) and (4, 4).
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