In an extreme ultraviolet light generation apparatus, a target detection section may include a light source, a transfer optical system, an image sensor configured to output image data of an image that has been formed by irradiating a target outputted from a target supply device with light outputted from the light source on a light-receiving unit of the image sensor by the transfer optical system, and a processing unit, connected to the image sensor, configured to receive the image data, obtain a first optical intensity distribution along a first line that intersects with a trajectory of the target and a second optical intensity distribution along a second line that intersects with the trajectory, calculate a center of gravity position in the first optical intensity distribution and a center of gravity position in the second optical intensity distribution, and calculate an actual path of the target based on the calculated positions.