Question

1. What is the equation of a circle with center (1, 3) and radius 4?

Answer 1

Given :-

• Centre = (1,3)
• radius = 4 units

To find :-

• Equation of the circle

Concept used :-

Equation of a circle with centre(a,b) and radius r units :-

➡️ ( x − a )² + ( y − b )² = r²

Solution :-

centre = (1,3)

radius = 4 units

➡️ ( x − a )² + ( y − b )² = r²

➡️ ( x − 1 )² + ( y − 3 )² = 4²

➡️ x²+1-2x+ y²+ 9-6y = 16

➡️ x²-2x+ y²+ 10 -6y = 16

➡️ x²-2x+ y²+ 10 -6y - 16=0

➡️ x²-2x+ y² -6y - 6=0

➡️ x²+ y² -2x -6y - 6=0

Answer :-

Equation of a circle with center (1, 3) and radius 4 :-

x²+ y² -2x -6y - 6=0

Answer 2

the general equation of a circle with center at (a,b) and radius r is

(x−a)² + (y−b)² = r²

so substituting the values we get the circle equation as

(x−1)² + (y+3)² = 25