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AB (= 10 unit) is diameter of a circle with center at point P = (x, 0) and point B = (0, y). The relation between x and y is:

AB (= 10 unit) is diameter of a circle with center at point P = (x, 0) and point B = (0, y). The relation between x and y is: Distance Formula, Concise Mathematics Solutions ICSE Class 9.

  1. x + y = 10

  2. x + y = 25

  3. x2 + y2 = 5

  4. x2 + y2 = 25

Distance Formula

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Answer

Given, AB is diameter of a circle with center at point P = (x, 0) and point B = (0, y).

By distance formula,

Distance between two points = (x2−x1)2+(y2−y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

From figure,

AB (Diameter) = 2 x PB (Radius)

⇒10=2×(x−0)2+(0−y)2⇒102=x2+(−y)2⇒5=x2+y2⇒52=x2+y2⇒x2+y2=25.\Rightarrow 10 = 2 \times \sqrt{(x - 0)^2 + (0 - y)^2}\\[1em] \Rightarrow \dfrac{10}{2} = \sqrt{x^2 + (-y)^2}\\[1em] \Rightarrow 5 = \sqrt{x^2 + y^2}\\[1em] \Rightarrow 5^2 = x^2 + y^2\\[1em] \Rightarrow x^2 + y^2 = 25.

Hence, option 4 is the correct option.

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