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How do you find an equation of a circle with the center and tangent?

How do you find an equation of a circle with the center and tangent?

The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

What is the general equation of the circle that has its center at (- 1/4 and tangent to y-axis?

Answer and Explanation: Therefore, the equation of the circle can be written as: {eq}(x-(-1))^2 + (y-4)^2 = r^2…

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How can you tell by looking at the equation of a circle that the center of the circle lies on the y-axis?

When the centre of a circle is on the y-axis i.e., h = 0. If the centre of a circle be on the y-axis, then the x co-ordinate of the centre will be zero. Hence, the general form of the equation of the circle will be of the form x2 + y2 + 2fy + c = 0, where g and c are the constants.

What does tangent to the line y 3 mean?

When a circle is tangent to a line, the line is perpendicular to the radius at the point of tangency. So since this circle is tangent to the y-axis at y=3, the y-coordinate of the center of the circle must also be 3.

What is the center of the circle?

The center of a circle is the point equidistant from the points on the edge. Similarly the center of a sphere is the point equidistant from the points on the surface, and the center of a line segment is the midpoint of the two ends.

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What’s the center of a circle called?

focus of the circle
The center of a circle is also called the focus of the circle. In general, a focus of a two-dimensional shape is a point that can be used to define…

Which is correct Centre or center?

Center and centre have the same meaning. Center is the correct spelling in American English, while in British English centre is correct. Notice that center (and centre) can be a noun, adjective, or a verb.

How to find the equation of the circle C?

Example In the diagram, the line L: 3x + y — 10 =0 is a tangent to the circle C. Find the equation of the circle C Solution: As the centre of the Circle C is (0, 0), its equation is of the form x2 We need to find the value of r.

How to find the centre and radius of each circle?

Thus, the equation of the clrcle is x2 +Y2= 17. 17) Example Find the centre and radius of each of the following circles: (ii) 4×2+4y2=25 (i) X2+Y2=8 25 25 Solution: 12 + y In the form x 2 + y the centre is (0, 0) r2=8 the radius IS 1,/@or 2V5.

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What is the center of a circle called?

was iorn and that er and COORDINATE GEOMETRY OF THE CIRCLE EQuation of a Circle, Centre (0, 0) and Radius r A circle is a set of points (a locus) which are equidistant from a fixed point called the ‘centre’. The distance from the centre to any point on the circle is called the ‘radius’.