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If the points A(4, 3) and B(x, 5) lie on the circle with center O(2,3), find the value of x. |
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Answer» Given that point A(4, 3) lies on a circle whose centre is O(2, 3). ∴ Distance between points O(2, 3) & A(4, 3) is equals to the radius of the circle. ∴ Radius of the circle is r = \(\sqrt{(4-2)^2+(3-3)^2}\) (By distance formula) Hence, the radius of the circle is r = 2 unit. Now, the equation of the circle whose centre is O(2, 3) and radius 2 is (x – 2)2 + (y – 3)2 = 22 ⇒ x2 – 4x + 4 + y2 – 6y + 9 = 4 (∵ (a – b)2 = a2 + b2 – 2ab) ⇒ x2 + y2 – 4x – 6y + 9 = 0. …(1) Since, point B(x, 5) lie on the circle whose equation given by equation (1), therefore, point B(x, 5) satisfies equation (1). ∴ x2 + 52 – 4x – 30 + 9 = 0 ⇒ x2 – 4x – 21 + 25 = 0 ⇒ x2 – 4x + 4 = 0 ⇒ (x – 2)2 = 0 ⇒ x – 2 = 0 ⇒ x = 2. Hence, the value of x is x = 2. |
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