Question

The centre of the circle is (-2,5) the point (4,5) lies on the circle . find the radius of the circle​

Answer 1

$\Large{\underbrace{\underline{\sf{Understanding\; the\; Question}}}}$

Here this is a question from coordinate geometry, where we have given coordinates of two points which are centre and a point on circumference of circle. As we know that when a line segment from centre meets the circle it is called it's radius. We can find radius of circle by finding the distance by distance formula of both given points.

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So let's start!

Given coordinates:

⇒The centre (-2,5)

⇒The point lies on circle (4,5)

Let us name these coordinates:

X1=-2

Y1=5

X2=4

Y2=5

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Now apply distance formula:

$\underline{\boxed{\sf{Distance\; Formula=\sqrt{(X2-X1)^{2}+(Y2-Y1)^{2}} }}}\star$

$\sf{Length\;of\; Radius=\sqrt{(4-2)^{2}+(5-5)^{2}} }$

$\sf{Length\;of\; Radius=\sqrt{(2)^{2}+(0)^{2}} }$

$\sf{Length\;of\; Radius=\sqrt{4+0} }$

$\sf{Length\;of\; Radius=\sqrt{4} }$

$\framebox{\boxed{\sf{Length\;of\; Radius=2\;Units}}}$

∵ Hence the required length of radius is 2 Units.