Question

Find the equation of the circle whose centre is (2,3) and which passes through the intersection of the lines 3x-2y-1=0 and 4x+y-27=0.​

Answer 1

Answer:

x²+y²-4x+6x-96=0

Step-by-step explanation:

Solving 3x – 2y = 1 and 4x + y = 27

Simultaneously, we get x = 5 and y = 7

∴ The point of intersection of the lines is (5, 7)

Now we have to find the equation of a circle whose centre is (2, -3) and which passes through (5, 7)

• Radius = √((5 - 2)²+ (7 + 3)²)
• = √(9 + 100)
• = √109

∴ Required equation of the circle is

(x – 2)² + (y + 3)²= (√109)²

x² + y²– 4x + 6y – 96 = 0