Let C be a circle in the family of concentric circles x2+y2=k2, where is a parameter. If C passes through (1,2), then the equation of C is

Question

Let C be a circle in the family of concentric circles x2+y2=k2, where is a parameter. If C passes through (1,2), then the equation of C is (A) x2+y2=5 (B) x2+y2=25 (C) x2+y2=√5 (D) x2+y2=4

Tardigrade Admin · Accepted Answer

Given equation of circle is x2+y2=k2. Since, it is passing through (1, 2). ∴ (1)2+(2)2=k2 ⇒ 1+4=k2 ⇒ k2=5 ∴ Required equation of circle is x2+y2=5.

Q. Let $C$ be a circle in the family of concentric circles $x^{2} + y^{2} = k^{2}$ , where is a parameter. If $C$ passes through $(1, 2)$ , then the equation of $C$ is

$x^{2} + y^{2} = 5$

$x^{2} + y^{2} = 25$

$x^{2} + y^{2} = 5$

$x^{2} + y^{2} = 4$

$x^{2} + y^{2} = 2$

Given equation of circle is $x^{2} + y^{2} = k^{2}$ .
Since, it is passing through (1, 2).
$∴ (1)^{2} + (2)^{2} = k^{2}$
$\Rightarrow 1 + 4 = k^{2}$
$\Rightarrow k^{2} = 5$
$∴$ Required equation of circle is $x^{2} + y^{2} = 5$ .

Q. Let C be a circle in the family of concentric circles x2+y2=k2, where is a parameter. If C passes through (1,2), then the equation of C is

x2+y2=5

x2+y2=25

x2+y2=5​

x2+y2=4

x2+y2=2

Given equation of circle is x2+y2=k2. Since, it is passing through (1, 2). ∴(1)2+(2)2=k2 ⇒1+4=k2 ⇒k2=5 ∴ Required equation of circle is x2+y2=5.

Q. Let $C$ be a circle in the family of concentric circles $x^{2} + y^{2} = k^{2}$ , where is a parameter. If $C$ passes through $(1, 2)$ , then the equation of $C$ is

$x^{2} + y^{2} = 5$

$x^{2} + y^{2} = 25$

$x^{2} + y^{2} = 5$

$x^{2} + y^{2} = 4$

$x^{2} + y^{2} = 2$

Given equation of circle is $x^{2} + y^{2} = k^{2}$ .
Since, it is passing through (1, 2).
$∴ (1)^{2} + (2)^{2} = k^{2}$
$\Rightarrow 1 + 4 = k^{2}$
$\Rightarrow k^{2} = 5$
$∴$ Required equation of circle is $x^{2} + y^{2} = 5$ .