Question

Circle with centre origin and passing through
(-1. 2) is​

Answer 1

Step-by-step explanation:

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Answer 2

The equation of the circle is x² + y² = 5

Given :

The circle with centre origin and passing through (-1,2)

To find :

The equation of the circle

Formula :

The equation of any circle with center (h,k) and of radius r is

(x - h)² + (y - k)² = r²

Solution :

Solution :Step 1 of 2 :

Assume the equation of the circle

Here it is given that the center of the circle is (0,0)

Let the equation of the circle is

$\displaystyle \sf{ {(x - 0)}^{2} + {(y - 0)}^{2} = {r}^{2} }$

$\displaystyle \sf{ \implies {x}^{2} + {y}^{2} = {r}^{2} } \: \: - - - - (1)$

Where r is the radius of the circle

Step 2 of 2 :

Find the equation of the circle

Since the circle passes through the point (-1,2)

Thus we get

$\displaystyle \sf{ {( - 1)}^{2} + {2}^{2} = {r}^{2} }$

$\displaystyle \sf{ \implies 1 + 4 = {r}^{2} }$

$\displaystyle \sf{ \implies {r}^{2} = 5}$

∴ The equation of the circle is x² + y² = 5

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