Find the equation of the locus of a moving point so that its distance from the point (1, 0) is always twice the distance from the point (0, –2).
3x2 + 3y2 + 2x + 16y + 15 = 0
Let (x1, y1) be the coordinates of the moving point whose locus is to be found.
distance from (1, 0) = 2 × (distance from (0, –2))
Replace x1 by x and y1 by y
Hence 3x2 + 3y2 + 2x + 16y + 15 = 0 is the equation of locus.
The number of integer values of m, for which the x-co-ordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:
The vertices of a triangles are A (x1, x1 tan α), B (x2, x2 tan β) and C (x3,x3 tan γ). If the circumcentre of Δ ABC coincides with the origin and H (a, b) be its orthocenter, then a/b is equal to:
A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinates axes at points P and Q. As L varies, the absolute minimum values of OP + OQ is (O is origin)
Consider the family of lines
(x + y – 1) + λ (2x + 3y – 5) = 0
and (3x + 2y – 4) + µ (x + 2y – 6) = 0
equation of a straight line that belongs to both the families is:
If p1, p2, p3 be the length perpendicular from the points
(m2, 2m), (mm’, m + m’) and (m’2, 2m’)
respectively on the line
The point (a2, a + 1) is a point in the angle between the lines 3x – y + 1 = 0 and x + 2y – 5 = 0 containing origin. Then ‘a’ belongs to the interval.
Find all points on x + y = 4 that lie at a unit distance from the line 4x + 3y– 10 = 0.
Find the equation of the obtuse angle bisector of the lines 12x – 5y + 7 = 0 and 3y – 4x – 1 = 0.
Find the bisector of the acute angle between the line 3x + 4y = 11 and 12x – 5y = 2.
A straight line drawn through point A (2, 1) making an angle π/4 with the +X-axis intersects another line x + 2y + 1= 0 in point B. Find the length AB.