Question

Find the equation of circle having center (6, 7) and radius 5.​

Answer 1

EXPLANATION.

Equation of circle having center ( 6,7).

Equation of circle having radius = 5.

General equation of circle,

⇒ x² + y² + 2gx + 2fy + c = 0.

Centre of circle = ( -g,-f).

radius of circle = r = √(g)² + (f)² - c = 0.

Equation of circle = ( x - α)² + ( y - β)² = a²

⇒ ( x - 6)² + ( y - 7)² = (5)².

⇒ x² + 36 - 12x + y² + 49 - 14y = 25.

⇒ x² + y² - 12x - 14y + 85 = 25.

⇒ x² + y² - 12x - 14y + 60 = 0.

                                       

MORE INFORMATION.

Different forms of the equation of circle.

(1) = Circle with center at the point (h, k ) and which touches the axis of x.

⇒ ( x - h)² + ( y - k)² = k².

(2) = Circle with center at the point ( h, k) and which touches the axis of y.

⇒ ( x - h)² + ( y - k )² = h².

(3) = Circle with radius a and which touches both the co-ordinate axis.

⇒ ( x ± a )² + ( y ± a )² = a²