Explain which trig functions and identities produce circles, ellipses and hyperbolas.

Step-by-step explanation:

The general equation for any conic section is:

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0,

where A, B, C, D, E, F are fixed coefficients and A, B, C are not simultaneously equal to 0.

But, we can also write equations for conic section in terms of trigonometric functions using Parametric Equations:

For circle:

(x, y) = (rcos(theta), rsin(theta)) <=> x^2 + y^2 = r^2,

because  (cos(theta))^2 + (sin(theta))^2 = 1

For ellipse:

(x, y) = (acos(theta), bsin(theta)) or x^2/a^2 + y^2/b^2 = 1

because  (cos(theta))^2 + (sin(theta))^2 = 1

For hyperbola:

(x, y) = (asec(theta), btan(theta)) or  x^2/a^2 - y^2/b^2= 1

because  (cos(theta))^2 + (sin(theta))^2 = 1

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

answer: it's upside down and i can't read it

step-by-step explanation: