JEE Advance - Mathematics (1990 - No. 7)
Let $${z_1}$$ = 10 + 6i and $${z_2}$$ = 4 + 6i. If Z is any complex number such that the argument of $${{(z - {z_1})} \over {(z - {z_2})}}\,is{\pi \over 4}$$ , then prove that $$\left| {z - 7 - 9i} \right| = 3\sqrt 2 $$.
The argument condition geometrically represents a circle passing through z1 and z2. The center of the circle can be determined by considering the geometry and is 7+9i. Then using the formula of the radius the given equation can be proved.
The argument condition geometrically represents a straight line passing through z1 and z2. The center of the circle can be determined by considering the geometry and is 7+9i. Then using the formula of the radius the given equation can be proved.
The argument condition geometrically represents a parabola passing through z1 and z2. The center of the circle can be determined by considering the geometry and is 7+9i. Then using the formula of the radius the given equation can be proved.
The argument condition geometrically represents a hyperbola passing through z1 and z2. The center of the circle can be determined by considering the geometry and is 7+9i. Then using the formula of the radius the given equation can be proved.
The argument condition geometrically represents an ellipse passing through z1 and z2. The center of the circle can be determined by considering the geometry and is 7+9i. Then using the formula of the radius the given equation can be proved.