A circle has the equation x^2 + y^2 = 9. (a) Find the center...

A circle has the equation $x^2 + y^2 = 9$. (a) Find the center $(h,k)$ and radius $r$ of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is (Type an ordered pair, using integers or decimals.)

Transcript

00:01 In this question, equation of a circle is given as x square plus y square minus 6x plus 2y plus 9 equals 0.

00:12 Now we have to find center and radius of the circle.

00:17 For finding center and radius we will write the given equation in its standard form.

00:21 Now let's rewrite the equation as x square minus 6x plus y square plus 2y equals minus 9.

00:34 Now we have to complete the square of x square minus 6x and y square plus 2y.

00:41 For that we will add 9 on both the sides of equation.

00:46 This will complete the square of x square minus 6x and we will add 1 on both the sides of the equation to complete the square of y square plus 2y.

00:56 Now this gives us x minus 3 whole square plus y plus 1 whole square is equal to 1 which can be written as 1 square now as we know standard form of an equation is x minus h whole square plus y minus k whole square is equal to r square where h comma k is the center and r is the radius now by comparing these two equations we can say center will be at 3.

01:34 Minus 1 and radius of the radius of the the circle will be equal to 1.

01:42 Now we have to graph the circle.

01:44 We will plot center of the circle which is at 3.

01:47 Minus 1.

01:49 Now we will consider 4 points which are at the distance of 1 unit from the center.

01:54 The first point on the right of the center which will be at 4...

Question

A circle has the equation $x^2 + y^2 = 9$. (a) Find the center $(h,k)$ and radius $r$ of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph. (a) The center of the circle is (Type an ordered pair, using integers or decimals.)

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