Question

PLEASE HELP!!!
Write the equation of the hyperbola where the foci are at (-5,4) and (-5,-10), and a=5.

Answer 1

centre at (0,0)??

Answer 2

No the center is at (-5, -3)

Answer 3

Center is mid point of foci i.e (-5,-3)

Answer 4

how did you find the midpoint of foci?

Answer 5

@ShailKumar

Answer 6

Mid point of two points (x1,y1) and (x2,y2) is ( (x1+x2)/2 , (y1+y2)/2 )

Answer 7

oh i see for the hyperbola is the center the same as h,k then?

Answer 8

yes

Answer 9

so then i have (x+5)^2+(y+3)^2=1 but its over a^2 and b^2 if we have a how do we find b? how can we find c to do the a^2+b^2=c^ thing?

Answer 10

This is a hyperbola of the form\[\frac{ (y-k)^{2} }{ a ^{2} }-\frac{ (x-h)^{2} }{ b ^{2} }=1\]

Answer 11

yes. But in this problem you cannot apply standard for of hyperbola.
Standard forms are meant for either horizontal or vertical hyperbola. This is not the case here.

Answer 12

*form

Answer 13

If this isn't a horizontal or a vertical hyperbola, then what kind is it?

Answer 14

Oh yes, its a vertical hyperbola

Answer 15

how do you know its a vertical hyperbola and why is that significant?

Answer 16

C is equal to the number of units up from the vertex the foci is. Here the foci is 7 units up and 7 units down from the vertex. So c = 7 c^2 = 49. a^2 + b^2= c^2...now fill in what you have. 49 = 25 + b^2 or 49 - 25 = b^2...24 = b^2. There's your b^2 for your formula.

Answer 17

so b is square root 24?

Answer 18

wai b^2 is just 24 and b is square root 24 right?

Answer 19

This is vertical because the foci lie on an "x = " line. The foci lie on the x = -5 line so it is a vertical hyperbola. It's important because the x^2 and the y^2 terms move according to which type of hyperbola it is. Like in an ellipse, the a^2 and b^2 move and the a^2 is always under the major axis. In hyperbolas, the y^2 coming first indicates the foci are on the y axis. The x^2 coming first indicates the foci are on the x axis. And yes, b is the square root of 24.

Answer 20

\[\frac{ (y+3)^{2} }{ 25 }-\frac{ (x+5)^{2} }{ 24 }=1\]

Answer 21

does it matter if you do the (y+3) or (x+5) first?

Answer 22

Remember the y axis is a vertical line. Look at a graph. And an x = something line is also a vertical line. But it's easier to remember the y^2 because the foci lie along the y axis, up and down, not side to side. Yes it matters very much if you do the (y + 3)^2 first; this indicates the way the hyperbola lie on the graph...it DEFINES the type of hyperbola it is.