SOLUTION: find the focus of the parabola that has the vertex (-3, 2) opens horizontally and passes through the point (-10, 1)

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Question 979291: find the focus of the parabola that has the vertex (-3, 2) opens horizontally and passes through the point (-10, 1)
Answer by MathLover1(20850) About Me  (Show Source):
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find the focus of the parabola that has the vertex (-3, 2) opens horizontally and passes through the point (-10, 1)
Standard form of equation for given parabola:
%28y-k%29%5E2=4p%28x-h%29, with (h,k)= (-3,+2) being the (x,y) coordinates of the vertex

For given equation:
%28y-2%29%5E2=4p%28x-%28-3%29%29
%28y-2%29%5E2=4p%28x%2B3%29
using given point (-10,1) to find 4p
%281-2%29%5E2%2F%28-10%2B3%29=4p
%28-1%29%5E2%2F%28-7%29=4p
4p=-1%2F7

Equation is:

%28y-2%29%5E2=4p%28x%2B3%29
%28y-2%29%5E2=-%281%2F7%29%28x%2B3%29
or
y=sqrt%28-%281%2F7%29%28x%2B3%29%29%2B2