Question

. Points A (-1,y) and B(5,7) lie on a circle with centre O(2, -3y). Find the values of y. Hence find the radius of the circle

Answer 1

Answer: y = 7, y = -1

Explanation:

Since both A and B lie on the circle, their distances to the origin is the radius which will be equal.

`d_(AO)=√((-1-2)^2+(y + 3y)^2)\\d_(BO)=√((5 - 2)^2+(7 + 3y)^2) \\\qquad \qquad \qquad \qquad d_(AO) = d_(BO)\\√((-1-2)^2+(y + 3y)^2)=√((5 - 2)^2+(7 + 3y)^2)\\√((-3)^2+(4y)^2)=√((3)^2+(7 + 3y)^2)\\√(9+16y^2)=√(9+(49+42y+9y^2))\\√(9+16y^2)=√(58+42y+9y^2)\\(√(9+16y^2))^2=(√(58+42y+9y^2))^2\\\\9+16y^2=58+42y+9y^2\\7(y^2-6y-7)=0\\7(y - 7)(y + 1)=0\\y - 7 = 0 \qquad\text{and}\qquad y + 1 = 0\\\quad y = 7 \qquad \text{and}\qquad y = -1`