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the latus rec tum of parabola with equation (x-1)^2 = -16(y-4) coincides with the diameter of a circle. find equation of circle?

Jan 23, 2018

#1
+101725
+2

the latus rec tum of parabola with equation (x-1)^2 = -16(y-4) coincides with the diameter of a circle. find equation of circle?

Consider the parabola

it is of the from     \((x-h)^2=4a(y-k)\)

Vertex  \((h,k) = (1,4)\)

Focal length = a = -4

So it is a concave down parabola with focus point  x=1 and y=4-4=0     focus (1,0)

The latus r****m is 16 units across and that is the diameter of the circle.

So the radius of the circle is 8 units and the centre of the circle is (1,0)

Circle:

\((x-1)^2+y^2=64\)

Jan 23, 2018
#2
+101725
+1

I just realized that you posted this question twice in quick succession.

If your question has been there a long time then you can make a knew post that directs people to the original post.

Just copy and post the address of the original post in with a short explanation.

A long time is subjective but there should be either a day or around 20 questions between the two .

Jan 23, 2018