Question

LOCATE THE POSITION OF POINT(2,4) CIRCLE x²+Y2-4X-6Y+11=0

Answer 1

Answer:

-1

Step-by-step explanation:

4+16-8-24+11

31-32

-1

Answer 2

The given point lies inside the circle.

Given,

Point → (2, 4)

Circle → x² + y² - 4x - 6y + 11 = 0

To Find,

Location of point wrt circle

Solution,

Firstly we will find the center and the radius of the circle.

General Equation of circle ⇒ x² + y² + 2gx + 2fy + c = 0

Center of circle = (-g, -f)

Radius of circle = $\sqrt{g^2+f^2-c}$

Comparing the given equation with the general equation, we get

g = -2, f = -3, c = 11

Center = (2, 3)

Radius = $\sqrt{(-2)^2+(-3)^2-11} = \sqrt{4 + 9 -11}$ $= \sqrt{2}$ units

Now, we will calculate the distance between the given point and the center -

Distance = $\sqrt{(2-2)^2 + (4-3)^2}$ = $\sqrt{0^2 + 1^2 } = 1$ units

Since the distance is less than the radius we can conclude that the given point lies inside the circle.

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