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Find the equation of a circle which touches both axes and passing through the point(2,1).

Find the equation of a circle which touches both axes and passing through the point(2,1).

Grade:12

1 Answers

Adithya Venkateswaran
20 Points
7 years ago
A circle which touches both the axes has intercept r on both axes i.e. the centre is at (r,r) after drawing the perpendicular from the axes at point of intersectionTherefore the equation simplifies to(x-r)² + (y-r)² = r²x² + y² + r² = 2r(x+y)Substituting the given pt (2,1)4+1+r² = 2r(3)r² - 6r + 5 = 0(r-5)(r-1) = 0r = 5r = 1x² + y² - 10(x+y) + 25 = 0x² + y² - 2(x+y) + 1 = 0

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