To the lines ax2 + 2hxy + by2 = 0, the lines a2x2 + 2h(a + b) xy + b2y2 = 0 are
equally inclined
perpendicular
bisector of the angle
None of these
If R be a realtion from A = {1, 2, 3, 4} to B = {1, 3, 5} such that (a, b) ∈R , then ROR-1 is
{(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)}
{(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)}
{(3, 3), (3, 5), (5, 3), (5, 5)}
{(3, 3), (3, 4), (4, 5)}
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. What is its y intercept
1/3
2/3
1
4/3
The number of common tangents to the circles x2 + y2 = 4 and x2 + y2 - 6x - 8y = 24 is
0
1
3
4
B.
1
The centres of the given circles x2 + y2 = 4 and x2 + y2 - 6x - 8y = 24 are C1(0, 0) and C2(3, 4) respectively. Their radii are r1 = 2 and r2 = 7 respectively.
We have, C1C2 = 5 < sum of radii
But C1C2 = difference of radii
Thus, the given circles touch each other internally.
Hence, the number of common tangent is only one.