Question

Find the equation of circle passing through (3,4) and having the centre at (-3,4)
Find the equation of circle whose centre is (-4,-3) and which passes through the origin.

Answer 1

Step-by-step explanation:

Question:

• Find the equation of circle passing through (3,4) and having the centre at (-3,4).

Solution:

Given that centre of circle c(-3,4) and point of circle p(3,4)

Radius of circle r = CP = √(3+3)² + (4-4)²

• 6

∴ Equation of circle :

• (x - h)² + (y - k)² = r²

⇒ (x + 3)² + (y - 4)² = (6)²

⇒ x² + y² + 6x - 8y - 11 = 0

Question:

• Find the equation of circle whose centre is (-4,-3) and which passes through the origin.

Solution:

Centre of the circle is c = (-4,3)

The circle passes through O(0,0) [Origin]

Radius of circle r = OC

⇒ r = √16 + 9

• 5

∴ Equation of circle :

• (x - h)² + (y - k)² = r²

⇒ (x + 4)² + (y + 3)² = 25

⇒ x² + y² + 8x + 6y = 0