Question
Download Solution PDFIf centre of the circle lies on the intersection of lines x + y = 1 and y = 2 and also cuts the circle x2 + y2 = 9 orthogonally then find the equation of the circle.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Condition of orthogonality = 2g1g2 + 2f1f2 = c1 + c2
Calculation:
Centre lies on intersection of lines x + y = 1 and y = 2,
So point of intersection = (-1, 2) = (-g, -f)
So g = 1, f = -2
Given circle = x2 + y2 - 9 = 0
Lets equation of that orthogonal circle is x2 + y2 + 2gx + 2fy + c = 0
Checking for the condition 2g1g2 + 2f1f2 = c1 + c2
⇒ 2. g. (0) + 2. f. (0) = c - 9
⇒ c = 9
So g = 1, f = -2 and c = 9
Radius of circle =
This will be an imaginary number, so circle can’t be made.
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