Question: why do trace and soho telescopes use special mirrors?
About the article "Telescope", section "Types".

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The name "telescope" covers a wide range of instruments.
Most detect electromagnetic radiation, but there are major differences in how astronomers must go about collecting light (electromagnetic radiation) in different frequency bands.
Telescopes may be classified by the wavelengths of light they detect:
 X-ray telescopes, using shorter wavelengths than ultraviolet light
 Ultraviolet telescopes, using shorter wavelengths than visible light
 Optical telescopes, using visible light
 Infrared telescopes, using longer wavelengths than visible light
 Submillimetre telescopes, using longer wavelengths than infrared light
As wavelengths become longer, it becomes easier to use antenna technology to interact with electromagnetic radiation (although it is possible to make very tiny antenna).
The near-infrared can be handled much like visible light, however in the far-infrared and submillimetre range, telescopes can operate more like a radio telescope.
For example the James Clerk Maxwell Telescope observes from wavelengths from 3 μm (0.003 mm) to 2000 μm (2 mm), but uses a parabolic aluminum antenna.
On the other hand, the Spitzer Space Telescope, observing from about 3 μm (0.003 mm) to 180 μm (0.18 mm) uses a mirror (reflecting optics).
Also using reflecting optics, the Hubble Space Telescope with Wide Field Camera 3 can observe from about 0.2 μm (0.0002 mm) to 1.7 μm (0.0017 mm) (from ultra-violet to infrared light).
 Fresnel Imager, an optical lens technology
 X-ray optics, optics for certain X-ray wavelengths
Another threshold in telescope design, as photon energy increases (shorter wavelengths and higher frequency) is the use of fully reflecting optics rather than glancing-incident optics.
Telescopes such as TRACE and SOHO use special mirrors to reflect Extreme ultraviolet, producing higher resolution and brighter images then otherwise possible.
A larger aperture does not just mean more light is collected, it is collected at a higher diffraction limit.
Telescopes may also be classified by location: ground telescope, space telescope, or flying telescope.
They may also be classified by whether they are operated by professional astronomers or amateur astronomers.
A vehicle or permanent campus containing one or more telescopes or other instruments is called an observatory.
X-ray telescopes can use a variety of different designs to image X-rays.
The most common methods used in X-ray telescopes are grazing incidence mirrors and coded apertures.
The limitations of X-ray optics result in much narrower fields of view than visible or UV telescopes. 
The largest optical telescope in the world as of 2009 to use a non-segmented single-mirror as its primary mirror is the 8.2 m (8.7 yards) Subaru telescope of the National Astronomical Observatory of Japan, located in Mauna Kea Observatory on Hawaii since 1997; however, this is not the largest diameter single mirror in a telescope, the U.S./German/Italian Large Binocular Telescope has two 8.4 m (9.2 yards) mirrors (which can be used together for interferometric mode).
Both of these are smaller than the 10 m segmented primary mirrors on the two Keck telescope.
Radio and submillimeter telescopes use much larger dishes or antennae, which do not have to be made as precisely as the mirrors used in optical telescopes.
The Hubble Space Telescope has a 2.4 m (7 ft 10 in) primary mirror. 
Dedicated infrared telescopes require a high and dry location, special instrumentation, and similar high-quality mirrors and optics as for visible wavelength observations.
Other large optical infrared and near-infrared telescopes circa 1980:There have been two other smaller near-infrared telescopes: the Gornergrat Infrared Telescope in the Swiss Alps, and the telescope at the Mont Mégantic Observatory in Canada. 
Generally, a spin-cast paraboloid is not sufficiently accurate to permit its immediate use as a telescope mirror or lens, so it is corrected by computer-controlled grinding machines.
The amount of grinding done, and the mass of glass material wasted, are much less than would have been required without spinning.
Spin casting can also be used, often with materials other than glass, to produce prototype paraboloids, such as spotlight reflectors or solar-energy concentrators, which do not need to be as exactly paraboloidal as telescope mirrors.
Spin casting every paraboloid that is made would be too slow and costly, so the prototype is simply copied relatively quickly and cheaply and with adequate accuracy.
Liquid mirror telescopes have rotating mirrors that consist of a liquid metal such as mercury or a low-melting alloy of gallium.
The mirrors do not solidify, but are used while liquid and rotating.
The rotation shapes them into paraboloids that are accurate enough to be used as primary reflectors in telescopes.
No correction of the shape is necessary.
Spin-cast glass mirrors need correction because of distortions that arise during and after solidification.