Correct Answer  Option 3 : ellipse
CONCEPT:
Simple Harmonic Motion (SHM):
 The Simple Harmonic Motion is studied to discuss the periodic Motion Mathematically.
 In Simple Harmonic motion, the motion is between two extreme points, and the restoring force responsible for the motion tends to bring the object to a mean position.
 The motion of a Simple pendulum and a block attached to spring are common examples of SHM.
Mathematically, SHM is Defined as:
x = A Sin (ωt + ɸ)  (1)
A is amplitude, ω is the angular frequency, ϕ is the phase difference.
The speed in SHM is given as

The Potential energy of the body in SHM is
P = \(\frac{1}{2}mω ^{2}x^{2}\)
 Kinetic Energy of the body in SHM is
K = \(\frac{1}{2}mω ^{2}(A^{2}x^{2})\)
So, Speed is given as
v ^{2} = ω ^{2} (A^{2}  x ^{2} )
CALCULATION:
Velocity is given as
\(v = \omega \sqrt{A^2  x^2}\)
Squaring
v 2 = ω 2 (A2  x 2 )
Dividing by ω 2 A2 both side
\(\implies \frac{v^2}{\omega^2 A^2} = 1 \frac{x^2}{A^2}\)
\(\implies \frac{v^2}{\omega^2 A^2} + \frac{x^2}{A^2}= 1\)
This is the equation of an ellipse.
So, the correct option is an ellipse.