SOLUTION: More hard ones. 1. What is the midpoint of the segment joining (3, 5) and (-6, 11)? 2. What is the distance between the points (-7, 7) and (-4, 11)? 3. What is the distanc

Question 2234: More hard ones.
1. What is the midpoint of the segment joining (3, 5) and (-6, 11)?
2. What is the distance between the points (-7, 7) and (-4, 11)?
3. What is the distance between the points (-2sqrt7, 10) and (4sqrt7, 8)?

4. What is the directrix of the parabola with the equation y+3=1/10(x+2)^2 ?
5. What is the axis of symmetry of the parabola with the equation
x-4=1/4(y+1)^2 ?

6. Find the vertices of a hyperbola with the equation (x+3)^2-4(y-2)^2=4.
7. Find the foci of a hyperbola with the equation 9y2-72y-16x2-64x-64=0.
8. Find the slopes of the asymptotes of a hyperbola with the equation y^2=36+4x^2.
9. What is the graph of the equation 6x^2-24x-5y^2-10y-11=0 ?
10. What is the graph of the equation 5x^2+2y^2+30x-16y+67=0 ?
11. What is the graph of the equation x^2+y^2-8x+6y+24=0 ?
12. What is the graph of the equation x^2+2x+7-y=0 ?
13. Identify the solutions to the system of equations:
x^2 + y^2 = 25
16x^2 + 25y^2 = 400
14. Identify the solutions to the system of equations:
y^2 - x^2 = 16
x^2 - y^2 = 16
Thanks you guys. Your pretty much are helping me through school.

Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
1. midpoint is (-1.5, 8)...do x and y midpoints separately.
2. length of difference between x values is 3. Length of difference between y values is 4. These form 2 sides of a right-angles triangle, so the distance between the 2 points is given by Pythagoras' Theorem...answer is 5 (3,4,5 triangle).
3. diff in x=6. Diff in y=2, so disntance is sqrt(36+4) etc...
the graphs...put x=0..find y and vice versa. Differentiate to find turning points, where applicable.
13. sub eqn1 into 2 for the x^2...you get that y=0. Sub this into 1, you get that x is +5 or -5.
14. Again, eqn1 subbed into 2 gives x=+4 or -4. Either solution gives y=0.
jon.
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