Question
Mathematics Question on Differential equations
For the real parameter t, the locus of the complex number z=(1−t2)+i1+t2
A
(A) an ellipse
B
(B) a parabola
C
(C) a circle
D
(D) a hyperbola
Answer
(B) a parabola
Explanation
Solution
Explanation:
Given z=(1−t2)+i1+t2Let z=x+ iyx=1−t2y2=1+t2Thus, x+y2=2y2=2−xy2=−(x−2)Thus parabola