The foci of the hyperbola whose equation is (1,−7) and (11,−7).
The hyperbola is horizontal, we will count 5 spaces left and right and plot the foci there.
We need to use the formula [tex]\rm c^ 2 =a^ 2 +b^ 2[/tex] to find c.
The given equation of the hyperbola is;
[tex]\rm \dfrac{(x-6)^2}{16}-\dfrac{(y+7)^2}{9}=1[/tex]
Here a^2 is 16 and b^2 =9.
Substitute all the values in the formula
[tex]\rm c^ 2 =a^ 2 +b^ 2\\\\\rm c^ 2 16+9\\\\\rm c^2=25\\\\c^2=5^2\\\\c=5[/tex]
The center of the hyperbola is (6, -7).
The foci of the hyperbola whose equation is;
( 6 +5 , -7), (6-5, -7)
(11, -7), (1, -7)
Hence, the foci of the hyperbola whose equation is (1,−7) and (11,−7).
Learn more about hyperbola here;
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