How are the points \[\left( {{\mathbf{1}}, - {\mathbf{3}}} \right),\left( { - {\mathbf{2}}, - {\mathbf{2}}} \right)\] and \[\left( {{\mathbf{0}}, - {\mathbf{3}}} \right)\;\] situated with respect to the circle \[{x^2} + {y^2} + {\mathbf{2}}x-y + {\mathbf{3}} = {\mathbf{0}}\].
Last updated date: 15th Mar 2023
•
Total views: 306k
•
Views today: 7.85k
Answer
306k+ views
Hint : In order to solve this problem put the given coordinates in the given circle and then observe the value, if it is greater than, less than or equal to zero then the point is outside, inside or on the circle respectively.
Given equation is \[{x^2} + {y^2} + 2x-y + 3 = 0\]
Let \[A = \left( {1, - 3} \right),B = \left( { - 2, - 2} \right)\;\] and \[C = \left( {0, - 3} \right)\]
We will satisfy these points on the given circle if the value is greater than zero then the point lies outside the circle , if it is equal to zero then the point lies on the circle and if less than zero then the point is inside the circle.
For point \[A\left( {1, - 3} \right),\,\,\,\,{x^2} + {y^2} + 2x-y + 3 = 1 + 9 + 2 + 3 + 3 = 18 > 0\]
Hence point A lies outside the circle
For point \[B = \left( { - 2, - 2} \right),\,\,\,\,{x^2} + {y^2} + 2x-y + 3 = 4 + 4 - 4 + 2 + 3 = 9 > 0\]
Hence point B lies outside the circle
For point \[C = \left( {0, - 3} \right),\,\,\,\,{x^2} + {y^2} + 2x-y + 3 = 0 + 9 + 0 + 3 + 3 = 15 > 0\]
Hence point C lies outside the circle.
Note :- Whenever you have asked the location of points inside, on or out of the circle.
Then you have to satisfy the points in the circle, if the value is greater than zero then the point lies outside the circle , if it is equal to zero then the point lies on the circle and if less than zero then the point is inside the circle.
Given equation is \[{x^2} + {y^2} + 2x-y + 3 = 0\]
Let \[A = \left( {1, - 3} \right),B = \left( { - 2, - 2} \right)\;\] and \[C = \left( {0, - 3} \right)\]
We will satisfy these points on the given circle if the value is greater than zero then the point lies outside the circle , if it is equal to zero then the point lies on the circle and if less than zero then the point is inside the circle.
For point \[A\left( {1, - 3} \right),\,\,\,\,{x^2} + {y^2} + 2x-y + 3 = 1 + 9 + 2 + 3 + 3 = 18 > 0\]
Hence point A lies outside the circle
For point \[B = \left( { - 2, - 2} \right),\,\,\,\,{x^2} + {y^2} + 2x-y + 3 = 4 + 4 - 4 + 2 + 3 = 9 > 0\]
Hence point B lies outside the circle
For point \[C = \left( {0, - 3} \right),\,\,\,\,{x^2} + {y^2} + 2x-y + 3 = 0 + 9 + 0 + 3 + 3 = 15 > 0\]
Hence point C lies outside the circle.
Note :- Whenever you have asked the location of points inside, on or out of the circle.
Then you have to satisfy the points in the circle, if the value is greater than zero then the point lies outside the circle , if it is equal to zero then the point lies on the circle and if less than zero then the point is inside the circle.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
