Parabola is a curve of infinite extent and is not often obsened in real life as circles or shaight line are . However, the parabplaic curres are very important and have some vert good propertvies like the light raus reflected from parabolic surface passes through one foxed point. This property of parabola is luidely used in making lenses and in optics.
The brridges also take parabolic shape have been centuries lod. So, now let us start studying this interesting curre in more detail.
Parabola is locus of point which moves such that its distance from fixed point (focus) is always equat to its distance from fixed line (directrix) i.e. eccentricity, e = 1 .
Note: The distance from fixed point to the distance from fixed line is calle
General second degree equation: eccentncity.
The equation ax2 by + 2hxy + 2gx + 2fy + c = 0
(1) Second degrel thrms make a perfict square. or n 2 = ab.
Why ?
Let the fixed point be . and fixed line ax + by + 1 = 0 Let variable point be (h,k).
Now,according to the definition of parabola.
the distance of (h,K) from () is same as distance from line ax + by + 1 = 0.
. and fixed line ax + by + 1 = 0 Let variable point be (h,k).
=(ax + by + 1)2
