NUMBER 3to 8 Answer and Explanation. 1. Find the angle, e, between the lines 3x
ID: 2912643 • Letter: N
Question
NUMBER 3to 8 Answer and Explanation.
1. Find the angle, e, between the lines 3x + 4y 12 and 4x 3y 12 2. Find the distance between the point (5, -9) and the line 3 Ty 21 3. Find the vertex, focus and directrix of the parabola 6x - 4y 10. 4. Find an equation of the parabola with its vertex at (2.-5) and focus at (2, -6). 5. Find the center, foci, vertices, and eccentricity of the ellipse + 4y2 -2x 32y61 0. . Find an equation of the ellipse with vertices (0, +6) and eccentricity e 7. Find the center, vertices, foci, and asymptotes of the hyperbola 16y2 --x 128y2310 8. Find an equation of the hyperbola with vertices at (+3,2) and foci at (5, 2). 9. Rotate the axes to eliminate the xy-term. Sketch the graph of the resulting equation, showing both sets of axes. 5r' + 2xy + 5y2-10 = 0 10. Use the discriminant to determine whether the graph of the equation is a parabola, ellipse, or hyperbola. (b) 4xy +4y - x - y + 17-0 11. Convert the polar point to rectangular coordinates. 2. Convert the rectangular point3-1) to polar coordinates. 13. Convert the rectangular equation 4x-3y-12 to polar form. 14. Convert the polar equationr 5 cos 8 to rectangular form. 15. Sketch the graph of r 1-cos ? 16. Sketch the graph of 5 sin 28. 17. Sketch the graph of r- 6-cos ? 18. Find a polar equation of the parabola with its vertex at 6 and focus at (0, 0) For Exercises 19 and 20, eliminate the parameter and write the corresponding rectangular equation.Explanation / Answer
3) x^2 - 6x - 4y + 1 = 0
(x^2 - 6x ) - 4y + 1 = 0
( x - 3)^2 - 9 - 4y + 1 = 0
( x- 3)^2 - 8 = 4y
dividing both sides by 4
y = 1/4 ( x- 3)^2 - 2
vertex = ( 3 , -2 )
4p = 4
p = 1
foci = ( 3 , -2 + p )
= ( 3 , -1 )
directrix lies outside the parabola
directrix y = -2 - p
y = - 3
8) vertices = (+- 3 , 2) and foci = (+- 5, 2)
h + a = 3
k = 2
h + c = 5
h - c = -5
--------------
2h = 0
h = 0
c = 5
a = 3
b = sqrt ( 5^2 - 3^2 ) = 4
hence, equation is
(x^2 / 9) - (y-2)^2 / 16 = 1
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