Question

Please answer this as soon as possible ​

Answer 1

Answer:

It is given that , centre of circle in (0,0) and passes through the point

`((13)/(2),0)`.

`:.` Radius of circle = Distance between (0,0) and `((13)/(2),0)`

`= = sqrt ((13/(2))^(2))= (13)/(2)=6.5`

A point lie outside on or inside the circles of the distance of it from the centre of the circle is greater than equal to or less than radius of the circle.

Now , to get the correct option we have to check the option one by one.

(a) Distance between (0,0) and (-3,4,1)=

`=sqrt ((9)/(16)+1)

=sqrt((25)/(16))

=(5)/(4)=1.25lt6.5

So , the point `(-(3)/(4),1)` lies interior to the circle

.

(b) Distance between (0,0) and `(2,(7)/(3))

= sqrt((2-0)^(2)+((7)/(3)-0)^(2))`

`=sqrt(4+(49)/(9))=sqrt((36+49)/(9))`

`=sqrt((85)/(9))=(9.22)/(3)=3.1lt6.5`

So , the point `(2,(7)/(3))` lies inside the circle.

( c) Distance between (0,0) and `(5,(-1)/(2))=sqrt((5-0)^(2)+(-(1)/(2)-0)^(2))`

`=sqrt(25+(1)/(4))=sqrt((101)/(4))=(10.04)/(2)`

`rArr =5.02lt6.5`

So , the point `(5,-(1)/(2))` lies insids the circle.

(d) Distance between (0,0) and `(-6,(5)/(2))= sqrt((-6-0)^(2)+((5)/(2)-0)^(2))`

`=sqrt(36+(25)/(4))=sqrt((144+25)/(4))`

`sqrt((169)/(4))=(13)/(2)=6.5`

So , the point `(-6,(5)/(2))` lis an the circle i.e., does not lie interior to the circle.

Step-by-step explanation:

THERE MIGHT BE SOME MATHEMATICAL TYPING ISSUES BUT YOUR ANSWER IS

OPTION D WHICH IS THE CORRECT ANSWER

Answer 2

Step-by-step explanation:

heres ur answer... Option (d)