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Will give BRAINLIEST! For parametric equations x= a cos t and y= b sin t, describe how the values of a and b determine which conic section will be traced. Be precise with explanation PLEASE!

Respuesta :

The a and b determine how big or small the shape of the conic section is. 
For the different conic sections given through the equations 
Circle: x^2/a^2 + y^2/a^2=1 
Ellipse: x^2/b^2+y^2/a^2 = 1 
Hyperbola: x^2/a^2 - y^2/b^2 = 1 
When trying to isolate cos and sin from those equations to get cos^2t + sin^2 t = 1 you can determine the conic section when substituting cos t = x/a and sint = y/b into cos^2t+sin^2t square it and then refer to the conic section equations to determine the conic section. x defines the major axis and y is the minor axis. a and b provide the coordinate pairs

Answer:

Step-by-step explanation:

Given that a conic section has  parametric equations x= a cos t and y= b sin t,

Since only sum of squares of sin and cos =1 we find that out of conic sections, namely

parabola, circle, ellipse, hyperbola this can correspond only to ellipse or circle

Because parabola has only one variable in 2 degrees and hyperbola is difference of squares.

i) When a=b, we have this represents a  circle with radius a.

ii) When a>b, we get an ellipse horizontal with major axis horizontal and centre at the origin and vertex at (a,0) (-a,0) (0,b) (0,-b)

iii) When a <b, we get a vertical ellipse with major axis as y axis and vertices same as

(a,0) (-a,0) (0,b) (0,-b)

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