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A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be?
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A circle touches both the axis and the centre lies in the fourth quadr...
Equation of a Circle in the Fourth Quadrant
To find the equation of a circle that touches both the x-axis and the y-axis with its center in the fourth quadrant, we can follow these steps:
Step 1: Determine the Center of the Circle
- Since the circle touches both the x-axis and the y-axis, its center will lie at the point (r, -r), where r is the radius of the circle.
- In this case, the radius of the circle is given as 1. Therefore, the center of the circle will be (1, -1).
Step 2: Write the General Equation of a Circle
- The general equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2.
Step 3: Substitute the Values into the Equation
- Substituting the values of the center (1, -1) and the radius 1 into the general equation, we get:
(x - 1)^2 + (y + 1)^2 = 1.
Step 4: Simplify the Equation
- Expanding the equation, we get:
x^2 - 2x + 1 + y^2 + 2y + 1 = 1.
- Simplifying further, we have:
x^2 + y^2 - 2x + 2y + 1 = 0.
Therefore, the equation of the circle that touches both the x-axis and the y-axis with its center in the fourth quadrant and a radius of 1 is:
x^2 + y^2 - 2x + 2y + 1 = 0.
To find the equation of a circle that touches both the x-axis and the y-axis with its center in the fourth quadrant, we can follow these steps:
Step 1: Determine the Center of the Circle
- Since the circle touches both the x-axis and the y-axis, its center will lie at the point (r, -r), where r is the radius of the circle.
- In this case, the radius of the circle is given as 1. Therefore, the center of the circle will be (1, -1).
Step 2: Write the General Equation of a Circle
- The general equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2.
Step 3: Substitute the Values into the Equation
- Substituting the values of the center (1, -1) and the radius 1 into the general equation, we get:
(x - 1)^2 + (y + 1)^2 = 1.
Step 4: Simplify the Equation
- Expanding the equation, we get:
x^2 - 2x + 1 + y^2 + 2y + 1 = 1.
- Simplifying further, we have:
x^2 + y^2 - 2x + 2y + 1 = 0.
Therefore, the equation of the circle that touches both the x-axis and the y-axis with its center in the fourth quadrant and a radius of 1 is:
x^2 + y^2 - 2x + 2y + 1 = 0.
Community Answer
A circle touches both the axis and the centre lies in the fourth quadr...
(x-1)^2 +(y+1)^2=1
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A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be?
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A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be?.
A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle touches both the axis and the centre lies in the fourth quadrant if it's radius is 1,then its equation will be?.
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