coordinate geometry: circles - The circle C has equation x^2 + y^2 - 6x + 4y = 12. The point R lies on the positive y-axis and the angle PRQ = 90°. (a) Find the coordinates of R.

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

Step 1: Find of the position of the point. (inside, outside or surface of the circle)

NOTE: According to the "Angle in a semicircle theorem". (Since PQR = 90)

"An angle inscribed in a semicircle is always a right angle"

Step 2: Find the coordinates of the of the r lies on the circle

NOTE: If the line intersecting the y-axis then put x = 0 in the equation

If the line intersecting the x-axis then put y = 0 in the equation.

EXAMPLE: x^2 + y^2 - 6x + 4y = 12

Put x = 0 because the point on the y- axis

y^2 + 4y = 12

Step 3: Solve the quadratic equation to find the coordinates.

NOTE: Factorize the equation.

EXAMPLE: y^2 + 4y = 12

(y – 2)(y + 6) = 0.