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how to get the focus of parbola

 Dec 22, 2014

Best Answer 

 #2
avatar+961 
+8

If you have the equation of a parabola in vertex form y = a(x - h)2 + k, then the vertex is at (h, k) and the focus is (h, k + 1/(4a)). Notice that here we are working with a parabola with a vertical axis of symmetry, so the x-coordinate of the focus is the same as the x-coordinate of the vertex

 Dec 23, 2014
 #1
avatar+23246 
+8

If the equation is in the form:  y  =  a(x - h)² + k

then the vertex is the point (h, k) and the focal point is the point (h, k + 1/(4a)).

If you need further information, please repost with specific questions.

 Dec 23, 2014
 #2
avatar+961 
+8
Best Answer

If you have the equation of a parabola in vertex form y = a(x - h)2 + k, then the vertex is at (h, k) and the focus is (h, k + 1/(4a)). Notice that here we are working with a parabola with a vertical axis of symmetry, so the x-coordinate of the focus is the same as the x-coordinate of the vertex

shaniab29544 Dec 23, 2014
 #3
avatar+118608 
+5

if it is in the form     $$(x-h)^2=4a(y-k)$$

 

then the vertex is (h,k)

 

The focal length is    $$|a|$$              (note that a can be negative)

 

So the focus will be     $$(h, k+a)$$

 Dec 23, 2014

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