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If a circle has its centre on (2, 3) and intersects another circle x2 + y2 + 4x - 8y + 16 = 0 orthogonally, then what will be the equation of the circle?

If a circle has its centre on (2, 3) and intersects another circle x2 + y2 + 4x - 8y + 16 = 0 orthogonally, then what will be the equation of the circle? Correct Answer x<sup style="">2</sup> + y<sup style="">2 </sup>– 4x - 6y = 0

Concept:

Condition of orthogonality = 2g1g2 + 2f1f2 = c1 + c2

Calculation:

Lets equation of that orthogonal circle is x2 + y2 + 2gx + 2fy + c = 0

Given: centre of circle is (2, 3) and it intersects another circle x2 + y2 + 4x - 8y + 16 = 0 orthogonally.

So g1 = - 2, f1 = - 3, g2 = 2, f2 = - 4, c1 = c and c2 = 16

Applying condition of orthogonality with the given circle –

⇒ 2( - 2)(2) + 2.( - 3). ( - 4) = c + 16

⇒ c = 0

So desired equation will be x2 + y2 – 4x - 6y = 0

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