Mathematics - Online Test
is equal to
The equation of the line perpendicular to the given line is x - y + k = 0
Since it passes through the origin,
0 - 0 + k = 0
Therefore k = 0
Hence the equation of the line is x - y = 0
On solving these two equations we get x = 1 and y = 1
The point of intersection of these two lines is (1,1)
Hence the coordinates of the foot of the perpendicular is (1,1)
definition of
Hence F
are collinear vectors , because are parallel in direction and same magnitude.
The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle is
Since the circle passes through (0,0) the equation reduces to
c= 0 -----(1)
Since it passes through (1,0),
1 + 2g + c = 0
This implies g = -1/2
Since the circle touches the circle x2 + y2 = 9, their radii should be equal
2 = 3
Substituting the values and simplifying we get f =
Hence the centre is (1/2, )
Let is a prime number . then :
