What locus is represented by the equation
My Self Assessment
a) Case 1: If c = 0 then the given equation represents four lines perpendicular to Y–axis whose equations are x = a, x = −a, x = b, x = −b.
Case 2: If c ≠ 0 then (x2 – a2) (x2 – b2) = 0 and y2 – b2 = 0 ie. The given equation represents 8 points whose coordinates are (a, b), (−a, b), (b, b), (−b, b), (a, −b), (−a, −b), (b, −b), (−b, −b)
If the tangent to the curve xy + ax + by = 0 at (1, 1) is inclined at an angle tan−12 with the X–axis, then
a) a = 1, b = 2
b) a = 1, b = −2
c) a = −1, b = −2
d) a = −1, b = 2
Find the angles between the straight lines represented by
Show that the two straight lines make with the axis of x angles such that the difference of their tangents is 2.
Prove that the following equation represent a pair of straight lines: . Find also their point of intersection and the angle between them
Find the value of k so that the following equation may represent pair of straight lines:
What relations must hold between the coefficients of the equation so that it represents a pair of straight lines.
The equation of a pair of opposite sides of a parallelogram are and . Find the equation of diagonals.
Prove that the straight lines joining the origin to the point of intersection of the straight line x – y = 2 and the curve make equal angles with the axes.
What is represented by the locus
What is represented by the equation
Prove that the equation represents three lines through the origin.
Find the equation to the pair of straight lines joining the origin to the intersection of the straight line y = mx + c and the circle . Prove that they are at right angles if
Show that the straight lines joining the origin to the other two points of intersection of the curves whose equations are will be at right angles if
If the pair of straight lines and be such that each pair bisects the angle between the other pair, prove that pq = −1
Show that the pair is equally inclined to the same pair.
Find the equation of the ellipse referred to centre whose focii are the points (4, 0) and (−4, 0) and whose eccentricity is
Find the latus rectum, the eccentricity, and the coordinates of the focii, of the ellipse x2 + 3y2 = a2
