Precal questions????????????????

Question

1. simplify

(3 - !2) / (2!3 5)

! :radical sign

2. write and equation for parabola with focus (0,2) and directrix y= -2

3. Find the focus and directrix for the parabola y=(x^2)-4X 4

4. Find the vertices, foci, eccentricity, and sketch the ellipse. ((x^2)/36) ((y^2)/16)=1

5. Classify the conics given and why : (7x^2) - (12y^2) -14x 24y -28=0

6. Put in standard form and classify the conics

(x^2) (4y^2) 6x-8y 9=0

thank you i did all these problems but i dont know if i did them right

i will give the best answer and try to help u out on ur points on anyone who answers and explains it

thank you

Answer 1

1.  (3-√2)/(2√3+5)

= (3-√2)(2√3-5) / [(2√3+5)(2√3-5)]

= (6√3 -15 -2√6 -5√2) / (12-25)

= -(6√3 -15 -2√6 -5√2) /13

5.  The coefficients of x² and y² have opposite signs.

That means it is a hyperbola.

6.  x² + 4y² + 6x - 8y + 9 = 0

x²+6x + y²-8y = -9

x²+6x+9 + y²-8y+16 = -9+9+16

(x+3)² + (y-4)² = 16

This is a circle with center (-3,4) and radius 4.