## WRITE EQUATION OF CIRCLE GIVEN CENTER AND RADIUS WORKSHEET

Write equation of circle given center and radius worksheet :

Here we are going to see some practice questions on writing equation of circle with given center and radius.

(1)  Find the equation of the circle if the center and radius are (2, − 3) and 4 respectively.

(2)  Find the equation of the circle with center (-2, 5) and radius 3. Show that it passes through the point (2, 8).

## Equation of circle with center and radius - Examples

Question 1 :

Find the equation of the circle if the center and radius are (2, − 3) and 4 respectively.

Solution :

Since center of the circle is at the point (2, -3), the equation of the circle is

(x - h)2 + (y - k)2  =  r2

Here (h, k) ==>  (2, -3) and r  =  4

(x - 2)2 + (y - 3)2  =  42

By comparing (x - 2)and (y - 3)2 with the algebraic identity (a - b)2, we get

x2 - 2(x)(2) + 22 + y2 - 2(y)(3) + 32  =  42

x2 - 4x + 4 + y2 - 6y + 9  =  16

x2 + y2  - 4x - 6y + 13  =  16

x2 + y2  - 4x - 6y + 13 - 16  =  0

x2 + y2  - 4x - 6y - 3  =  0

Hence the required equation of the circle is x2 + y2  - 4x - 6y - 3  =  0

Example 2 :

Find the equation of the circle with center (-2, 5) and radius 3. Show that it passes through the point (2, 8).

Solution :

Since center of the circle is at the point (2, -3), the equation of the circle is

(x - h)2 + (y - k)2  =  r2

Here (h, k) ==>  (-2 , 5) and r  =  3

(x - (-2))2 + (y - 5)2  =  32

(x + 2)2 + (y - 5)2  =  32

By comparing (x + 2)and (y - 5)with the algebraic identity (a + b)2 and (a - b)2, we get

x2 - 2(x)(2) + 22 + y2 - 2(y)(5) + 52  =  32

x2 - 4x + 4 + y2 - 10y + 25  =  9

x2 + y2 - 4x - 10y + 29  =  9

x2 + y2 - 4x - 10y + 29 - 9  =  0

x2 + y2 - 4x - 10y + 20  =  0

Hence the required equation of the circle is x2 + y2 - 4x - 10y + 20  =  0

To show that the circle is passing through the point (2, 8), we need to apply this point in the above equation.

x = 2 and y = 8

22 + 82 - 4(2) - 10(8) + 20  =  0

4 + 64 - 8 - 80 + 20  =  0

88 - 88  =  0

0 = 0

Since the point (2, 8) satisfies the above equation, we can say that the point (2, 8) is passing through the circle.

After having gone through the stuff given above, we hope that the students would have understood "Write equation of circle given center and radius worksheet".

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