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

Q1:

Determine the equation of a circle that passes through the point π΄ ( 0 , 8 ) if its center is π ( β 2 , β 6 ) .

Q2:

Determine the equation of a circle that passes through the point π΄ ( 5 , 1 0 ) if its center is π ( 6 , 9 ) .

Q3:

Determine the equation of a circle that passes through the point π΄ ( 5 , β 1 0 ) if its center is π ( 2 , β 4 ) .

Q4:

Determine the equation of a circle that passes through the point π΄ ( 1 , 3 ) if its center is π ( 1 0 , β 3 ) .

Q5:

Determine the equation of a circle that passes through the point π΄ ( 8 , β 2 ) if its center is π ( 5 , β 8 ) .

Q6:

Determine the equation of a circle that passes through the point π΄ ( β 7 , 2 ) if its center is π ( β 3 , 2 ) .

Q7:

Determine the equation of a circle that passes through the point π΄ ( 9 , β 5 ) if its center is π ( β 6 , 1 0 ) .

Q8:

Determine the equation of a circle that passes through the point π΄ ( 4 , β 1 0 ) if its center is π ( β 3 , β 1 0 ) .

Q9:

Determine the equation of a circle that passes through the point π΄ ( 3 , β 4 ) if its center is π ( 0 , β 5 ) .

Q10:

Determine the equation of a circle that passes through the point π΄ ( 7 , β 5 ) if its center is π ( 7 , 2 ) .

Q11:

A circle has center ( 2 , 2 ) and goes through the point ( 6 , 3 ) . Find the equation of the circle.

Q12:

Determine the equation of a circle whose centre is at the point π ( 4 , β 3 ) , given that the circle touches the straight line π₯ = 1 0 .

Q13:

The given figure shows a circle with center π ( π₯ , π¦ ) 0 0 and a point π΄ ( π₯ , π¦ ) lying on the circumference of the circle.

Find the length of π π΅ in terms of π₯ and π₯ 0 .

Find the length of π΄ π΅ in terms of π¦ and π¦ 0 .

Using the Pythagorean Theorem, express π 2 in terms of the lengths of π π΅ and π΄ π΅ .

Q14:

A circle has center ( 4 , β 2 ) and goes through the point ( β 2 , β 3 ) . Find the equation of the circle.

Q15:

A circle centered at the origin goes through the point (1, 1).

Work out the equation of the circle.

Determine the positive value of π¦ when π₯ = 1 2 .

Is the point οΏ 1 2 , β 7 2 ο on the circle?

Q16:

A circle has center οΌ 2 3 , β 2 5 ο and goes through the point ( β 3 , 5 ) . Find the equation of the circle.

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