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?

Guest Jan 23, 2018

#1**+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:

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

Melody Jan 23, 2018

#2**+1 **

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

PLEASE DO NOT DO THAT!

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 .

Melody Jan 23, 2018