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Hyperbola

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The equation of the hyperbola shown below can be written as $$\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1.$$

Find h + k + a + b.

I've found k to be -1, y to be 3, and a is -2, but what is b and are my answers so far right?

May 7, 2019
edited by Lightning  May 7, 2019

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The center is   (h, k)  = ( -1,3)

One of the asymptotic lines- the one with a positive slope - passes through  ( 1, 6)  [ and the center]

So.....we can write an equation of this line.....the slope  =  [ 6 - 3 ] / [ 1 - - 1 ]  =  3/2

So.....we can write the eqation of this line as

y  =  (3/2)(x - -1) + k   =  (3/2) ( x + 1) + 3   =    (b/a) ( x - h) + k

So.....

a = 2    b   = 3    h  =  -1    and k  =  3        and their sum  = 7

Here's a graph : https://www.desmos.com/calculator/lxpgxphby3

May 7, 2019