Type the standard form of the equationType an equation Simpl

Type the standard form of the equation.__________(Type an equation. Simplify your answer.) Find the standard form of the equation of the hyperbola satisfying the given condition Endpoints of transverse axis: (0, -6), (0, 6); asymptote: y = 3x The equation is________. Find the standard form of the equation of the parabola satisfying the given condition Focus: (-4,0); Directrix: x -4 The equation of the parabola is_______.

Solution

18. Equation of hyperbola =

slope of the asymptote line of a hyperbola is the ratio b/a for a simple hyperbola of the form

(x^2/a^2(y^2/b^2)=1

So, given y=3x, we can see that the ratio b/a=3 Furthermore, we can say that b=3n a=n since the ns would cancel in the ratio.

Now that we have our a and b depending on only one variable n, we can use the relationship you mentioned, c^2=a^2+b^2, to determine the value of n.

a^2 + b^2 = c^2 i.e. n^2 + 9n^2 =c^2 ( as a=n, b=3n) i.e. 10n^2 = 36 i.e n =1.9

Therefore, we have a=1.9 and b=3n = 5.7, so then our equation for this hyperbola can be expressed with the following:

(x^2/1.9^2)(y^25.7^2)=1

i.e. 9x^2 - y^2 = 32.49

19. equation of parabola = (y^2 = -16x)