What Is The Meaning Of Conics?

What is the meaning of conics?

 

Answer:

Conics is a branch of Mathematics that it is concerned with Conic Sections.  It is a set of all points P in a plane such that the distance of P from a fixed point is in a constant ratio to the distance of P from a fixed line which does not  contain the fixed point. Conics can find on cones.

Step-by-step explanation:

There are 4 conic sections:

a. Circle - x² + y² = 1 (at the origin); (x-h)² + (y-k)² = 1 (not at the origin)

b. Ellipse - x²/a² + y²/b² = 1 (horizontal axis); x²/b² + y²/a² = 1 (vertical axis)

c. Parabola -

  1. y² = 4px); where the vertex is at the origin, focus at (0,p), directrix at y=-p
  2. (x-h)² = 4p (y-k); where the vertex at (h,k), the focus at (h, k+p), and the directrix at y=k-p

d. Hyperbola -

x²/a² - y²/b² = 1

where

  1. the length of the transverse axis is  2 a
  2. the coordinates of the vertices are  ( ± a , 0 )
  3. the length of the conjugate axis is  2 b
  4. the coordinates of the co-vertices are  ( 0 , ± b )
  5. the distance between the foci is  2 c , where  c ²= a ²+ b ²
  6. the coordinates of the foci are  ( ± c , 0 )
  7. the equations of the asymptotes are  y = ± b/ a  x

x²/b² - y²/a² = 1

where

  1. the length of the transverse axis is  2 a
  2. the coordinates of the vertices are  ( 0,±a )
  3. the length of the conjugate axis is  2 b
  4. the coordinates of the co-vertices are  (±b, 0   )
  5. the distance between the foci is  2 c , where  c ²= a ²+ b ²
  6. the coordinates of the foci are  (   0,±c )
  7. the equations of the asymptotes are  y = ± a/b  x


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