Hyperbola

Question

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887

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+1245

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?

Lightning May 7, 2019

edited by Lightning May 7, 2019

CPhill · Answer 1 · 2019-05-07T03:35:10

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