Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

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

Q1:

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

Q2:

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

Q3:

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

Q4:

What is the equation of the circle of centre ( 3 , 4 ) and passing through ( 7 , 7 ) ?

Q5:

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

Q6:

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?

Q7:

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 .

Q8:

The given figure shows a circle with center π ( π₯ , π¦ ) ο¦ ο¦ 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₯ ο¦ .

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

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

Q9:

Find the radius of the circle that passes through point ( β 3 , β 2 ) and has centre ( β 5 , 8 ) .

Q10:

Does the coordinate ( 3 , β 1 ) lie on the circle centred at the point ( 2 , β 2 ) passing through the point ( 1 , β 1 ) ?

Q11:

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

Q12:

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

Q13:

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

Q14:

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

Q15:

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

Q16:

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

Donβt have an account? Sign Up