Find the equation of the circle whose end points of a diameter are (4, 2), (1, 5).

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Q. Find the equation of the circle whose end points of a diameter are (4, 2), (1, 5).

Yanam BieapBIEAP Intermediate Board 2024Subjective· 2mImportance★★★★★

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The diametric-form equation $(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$ gives the circle directly from the two diameter endpoints.

If $(4,2)$ and $(1,5)$ are the ends of a diameter, any point $(x,y)$ on the circle sees them at a right angle, so

$(x-4)(x-1)+(y-2)(y-5)=0$

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Q.Find the equation of the circle whose end points of a diameter are (4, 2), (1, 5).