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If a Circle Passes Through the Point (0, 0),(A, 0),(0, B) Then Find the Coordinates of Its Centre. - Mathematics

If a circle passes through the point (0, 0),(a, 0),(0, b) then find the coordinates of its centre.

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Solution

The general equation of the circle is x2 + y2 + 2gx + 2fy c = 0
Now, it is passing through (0, 0)
∴ c = 0
Also, it is passing through (a, 0)
∴  a2 + 2ag = 0
⇒ a(a + 2g) = 0
a + 2g = 0

\[\Rightarrow g = - \frac{a}{2}\]

Again, it is passing through (0, b)
 b2 + 2bf = 0
⇒ b(b + 2f) = 0
b + 2f = 0

\[\Rightarrow f = - \frac{b}{2}\]

The coordinates of its centre are given by

\[\left( - g, - f \right) = \left( \frac{a}{2}, \frac{b}{2} \right)\]
Concept: Circle - Standard Equation of a Circle
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 24 The circle
Exercise 24.2 | Q 14 | Page 32
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