## Question

Find the locus of the point of intersection of the lines and where α is variable.

### Solution

Given equations are

Here is a variable on eliminating α. Squaring and adding (1) and (2), we get required locus as:

#### SIMILAR QUESTIONS

Consider the point then

A variable straight line of slope 4 intersects the hyperbola *xy* = 1 at two points. The locus of the point which divides the line segment between these two points in the ratio 1 : 2 is

Find the co – ordinates of the point which divides the line segment joining the pints (5, – 2) and (9, 6) in the ratio 3 : 1.

Find the co – ordinates of a point which divides externally the line joining (1, **–**3) and (**–**3, 9) in the ratio 1 : 3.

Two vertices of a triangle are (–1, 4) and (5, 2). If its centroid is (0, –3), find the third vertex.

Find the area of the pentagon whose vertices are A(1, 1), B(7, 21), C(7, –3), D(12, 2) and (0, –3).

Find the locus of a point which moves such that its distance from the point (0, 0) is twice its distance from the *y *– axis.

Find the equation of the curve 2*x*^{2} + *y*^{2} – 3*x *+ 5*y *– 8 = 0 when the origin is transferred to the point (–1, 2) without changing the direction of axes.

Given the equation through what angle should the axes be rotated so that the term in *xy *be waiting from the transformed equation.

Find the locus of a point whose co – ordinate are given by *x *= *t *+ *t*^{2}, *y *= 2*t *+ 1, where *t *is variable.