How do you find the equation of a circle touching the x-axis?

We will learn how to find the equation of a circle touches x-axis. The equation of a circle with centre at (h, k) and radius equal to a, is (x – h)2 + (y – k)2 = a2. When the circle touches x-axis i.e., k = a.

What does it mean when a circle touches the x-axis?

(h,k) is the center of the circle. In this example, touching the x-axis also means the x axis is tangent to the circle, where y = 0. This also means it is perpendicular to the radius.

What is the parametric equation of circle?

The equation of a circle in parametric form is given by x=acosθ , y=asinθ .

Which equation has a center at 2 1 and a point on the circle of 2/3 )?

The equation of the circle whose center is (2,1) and radius is 3 is (x – 2)2 + (y – 1)2 = 9.

What is the equation of a circle touching axis of X and Y with its radius 5?

The given radius of the circle is 5 units, i.e. . Thus, the equation of the circle is x 2 + y 2 + 10 x + 10 y + 25 = 0 .

What do you call the line that touches the circle at exactly one point?

A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

What is the radius of point circle?

The distance from a circle’s center to a point on the circle is called the radius of the circle. A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle. For the circle below, AD, DB, and DC are radii of a circle with center D.

How to find the equation of a line passing through a point?

The circle passing through (1, -2) and touching the axis of x at (3,0) also passes through the point. Medium View solution If the angle of intersection of the circles x2+y2+x+y=0and x2+y2+x−y=0is θ, then the equation of a line passing through (1,2)and making angle θwith the y-axis is

What are the coordinates of the center of the circle?

So, the coordinates of the centre of the circle is in the form of O, (3,-y). As it is known that the points lying on the circle are equidistant to its centre, A and B are equidistant to (3,-y).

What does the circle x2 + y2 = 4 cut?

The circle x 2 + y 2 = 4 cuts the line joining the points A (1, 0) and B (3, 4) in two points P and Q. Let P A B P ​ = α and Q A B Q ​ = β .