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In this lesson, we will learn how to find the equation of a circle using its center and radius.

Q1:

Write, in the form π π₯ + π π¦ + π π₯ + π π¦ + π = 0 ο¨ ο¨ , the equation of the circle of radius 10 and center ( 4 , β 7 ) .

Q2:

Write the equation of the circle of centre ( 0 , 5 ) and diameter 10.

Q3:

Give the general form of the equation of the circle centre ( 8 , β 2 ) and diameter 10.

Q4:

Find the general form of the equation of circle π , given that it touches the two coordinate axes at π΄ and π΅ and that π π = 6 β 2 .

Q5:

Write the equation of the circle of center ( 8 , 4 ) and radius 9.

Q6:

Determine the equation of a circle with radius = 1 7 c m , given that it touches the π¦ -axis at the point ( 0 , β 7 ) , and its centre lies in the third quadrant.

Q7:

What is the equation of the circle of radius 24 that lies in the third quadrant and is tangent to the two axes?

Q8:

Find the point of intersection between the line with equation π¦ = 1 2 5 π₯ β 2 6 and the circle with center ( β 2 , 3 ) and radius 13.

Q9:

Let us consider a circle of radius 4 and center ( 2 , β 7 ) .

Write the equation of the circle.

The circle is dilated by a factor of 2. The center of dilation is the center of the circle. Write the equation of the circle.

Q10:

Let us consider a circle of radius 6 and center ( β 2 , β 5 ) .

The circle is dilated by a factor of 1 3 . The center of dilation is the center of the circle. Write the equation of the circle.

Q11:

A circle is tangent to the π₯ -axis at ( 8 , 0 ) and cuts a chord of length 2 β 3 7 7 on the negative π¦ -axis. What is the equation of the circle?

Q12:

A circle of radius 39 length units has its centre π at the point ( β 1 1 , β 1 5 ) . Given that the circle intersects the π₯ -axis at points π΄ and π΅ , determine the area of β³ π π΄ π΅ .

Q13:

In the figure below, find the equation of the circle.

Q14:

Given π΄ ( 1 0 , 9 ) and π΅ ( 1 0 , β 1 ) , find the equation of the circle with diameter π΄ π΅ .

Q15:

Write, in the form π π₯ + π π¦ + π π₯ + π π¦ + π = 0 ο¨ ο¨ , the equation of the circle of radius 10 and center ( β 7 , β 8 ) .

Q16:

Write, in the form π π₯ + π π¦ + π π₯ + π π¦ + π = 0 ο¨ ο¨ , the equation of the circle of radius 4 and center ( β 6 , 3 ) .

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