Answer :25π The centre of the circle is(1,2) So, its equation is (x−1)2 + (y−2)2 = r2 It passes through(4,6) &there4;(4−1)2+(6−2)2 = r2 ⇒9+16=r2 &there4;

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Find the area of the circle centred at (1,2) and passing through (4,6)

Davneet Singh

Answer : $25 π$

The centre of the circle is $(1, 2)$

$(x - 1)^{2} + (y - 2)^{2} = a^{2}$

$(x - 1)^{2} + (y - 2)^{2} = a^{2}$

It passes through $(4, 6)$

$∴ (4 - 1)^{2} + (6 - 2)^{2} = a^{2}$

$\Rightarrow 9 + 16 = a^{2}$

$∴ a = 5$

$∴$ Radius $a = 5$

Hence the area of the circle is

$π a^{2} = π (5)^{2}$

$\Rightarrow 25 π$

Written on Oct. 31, 2019, 11:52 a.m.

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