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 \[{x^2} + {y^2} + {\mathbf{2}}x-y + {\mathbf{3}} = {\mathbf{0}}\].
Answer
364.2k+ 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.
Last updated date: 25th Sep 2023
•
Total views: 364.2k
•
Views today: 7.64k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE
