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jolli1 [7]
3 years ago
12

Write the following in both standard and general form

Mathematics
1 answer:
nalin [4]3 years ago
6 0

The circle equation in standard form: (x-3)^{2}+(y+2)^{2}=4^{2}

The circle equation in general form: x^{2}+y^{2}-6 x+4 y-3=0

<u>Solution:</u>

Given that, center of a circle is (3, -2) and radius = 4.

We have to find the standard and general form of the circle.

<em><u>Finding standard form:</u></em>

The standard form of circle is (x-h)^{2}+(y-k)^{2}=r^{2}

where (h, k) is center and r is radius.

So the standard form of circle is

\begin{array}{l}{\left.(x-3)^{2}+(y-(-2))\right)^{2}=4^{2}} \\\\ {\rightarrow(x-3)^{2}+(y+2)^{2}=4^{2}}\end{array}

<em><u>Finding general form:</u></em>

Now, we just have to expand the standard form to get the general form.

\begin{array}{l}{\text { So, }(x-3)^{2}+(y+2)^{2}=4^{2}} \\\\ {\rightarrow x^{2}+9-6 x+y^{2}+4+4 y=16} \\\\ {\rightarrow x^{2}+y^{2}-6 x+4 y+13-16=0} \\\\ {\rightarrow x^{2}+y^{2}-6 x+4 y-3=0}\end{array}

Hence the standard and general form are found out

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Step-by-step explanation:

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Rounding off will give: 2.24 units

The distance between both lines is 2.24 units

Keywords: Equations of lines

Learn more about distance in lines at:

  • brainly.com/question/7449065
  • brainly.com/question/7490805

#LearnwithBrainly

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