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A day full of math games & activities. Find one near you.
How to find the equation of a circle given the center(2, -1) and a point it passes through (3, 4)?
Solution:
The centre of the circle is given as (h, k) = (2, -1)
Since, the circle passes through the point (3,4), the radius (r) of the circle is the distance between the point (2, -1) and (3,4).
r = √(3 - 2)2 + (4 + 1)2
r = √1 + 25 = √26
The equation of the circle is (x - h)2 + (y - k)2 = r2
(x - 2)2 + (y + 1)2 = (√26)2
Expanding using the algebraic identity
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab
x2 + 4 - 4x + y2 + 1 +2y = 26
So we get
x2 - 4x + 2y + y2 + 5 = 26
Therefore, the equation of the circle is x2 - 4x + 2y + y2 - 19 = 0.
How to find the equation of a circle given the center(2, -1) and a point it passes through (3, 4)?
Summary:
The equation of a circle given the center(2, -1) and a point it passes through (3, 4) is x2 - 4x + 2y + y2 - 19 = 0.
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