20 years ahead

Geometry Level 2

If 4 y + 3 x = 2015 4y + 3x = 2015 and 3 x + 4 y − 2035 = 0 3x + 4y - 2035= 0 are equations of two tangents of a circle, then equation of this circle is:

7 x 2 + 7 y 2 + 5 x − 8 y = 0 7x^2 + 7y^2 + 5x - 8y = 0 Cannot be determined uniquely x 2 + y 2 − 9 x + 6 y = 2005 x^2 + y^2 - 9x+6y = 2005 3 x 2 + 3 y 2 − x + 6 y = 2025 3x^2 + 3y^2 - x +6y = 2025

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Ravneet Singh by Ravneet Singh , 30, India

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1 solution

Ravneet Singh
Dec 27, 2015

with the given information we can find the radius but we cannot find an exact coordinates of the centre....hence we cannot find a unique equation of the circle.

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For giggles, how would we express the radius?

Christian Brown - 5 years, 3 months ago

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Since both the given equations are parallel lines and also tangents to the circle, so distance between them is the diameter of circle

Ravneet Singh - 5 years, 3 months ago

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That makes perfect sense, thank you.

Christian Brown - 5 years, 3 months ago

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