Instructions: Graph the conic section and make sure to label the

facas9

facas9

Answered question

2021-08-10

Instructions:
Graph the conic section and make sure to label the coordinates in the graph. Give the standard form (SF) and the general form (GF) of the conic sections.
CIRCLES:
Center is at (2, 4). the diameter's length is 6. The endpoints of the diameter is at (1, 4) and (3, 6).

Answer & Explanation

Aubree Mcintyre

Aubree Mcintyre

Skilled2021-08-11Added 73 answers

Step 1
We have to find standard form and general form of conic section and also we have to make the graph of these conic.
Step 2
Centre (2, 4) and diameter's length is 6.
We have given diameter =6
So, radius of circle (r)=62=3
Concept:
If centre of a circle is (h, k) and radius of circle is r, then equation of circle in standard form is:
(xh)2+(yk)2=r2
And we can find general form of circle after expanding standard form:
We have centre of circle (2, 4) radius 3
So, equation of circle in standard form is:
(x2)2+(y(4))2=32 or (x2)2+(y+4)2=32
Now,
Expland (x2)2+(y+4)2=32 we get
x2+y24x+8y+4+16=9
x2+y24x+8y+11=0
So, general form of circle is:
x2+y24x+8y+11=0
Now, graph of this circle:
image

Step 3
End points of the diameter are (1, 4) and (3, 6)
Centre of circle lies on the mid-point of the diameter
So, centre of coordinate (x, y)=(312, 642)=(1, 1)
And distance between (1, 4) and (3, 6)
=(6(4))2+(3(1))2
=(6+4)2+(3+1)2
=100+16
=116
=229
Distance of diameter =229
So, radius of circle (r)=2292=29
We have centre (1, 1) and radius (r)=29
So, equation of circle in standard form is:
(x1)2+(y1)2=(29)2
Now,
Expand (x1)2+(y1)2

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