How do you find the equation of a circle given two points and a 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.

How do you find the equation of the tangent line to the origin of a circle?

The X coordinate of the centre of the circle is r and the radius of the circle is also r. With this information we can say that the circle will touch the Y axis. Which means that the equation of the first tangent from the origin to the circle will be $x = 0$. Now, let the equation of the second tangent be $y = mx$.

How do you find the gradient of a tangent to a circle?

To find the gradient use the fact that the tangent is perpendicular to the radius from the point it meets the circle. Work out the gradient of the radius (CP) at the point the tangent meets the circle. Then use the equation.

What is tangent equation?

Recall : • A Tangent Line is a line which locally touches a curve at one and only one point. • The slope-intercept formula for a line is y = mx + b, where m is the slope of the line and b is the y-intercept. • The point-slope formula for a line is y – y1 = m (x – x1). This formula uses a.

What is the equation for a circle passing through two points?

Equation of a Circle Through Two Points and a Line Passing Through its Center. Consider the general equation a circle is given by. x 2 + y 2 + 2 g x + 2 f y + c = 0. If the given circle is passing through two points, say A ( x 1, y 1) and B ( x 2, y 2), then these points must satisfy the general equation of a circle.

What is the equation of the tangent to a circle?

The equation of the tangent to a circle A tangent to a circle at point P with coordinates ((x, y)) is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P. As the tangent is a straight line, the equation of the tangent will be of the form (y = mx + c).

How do you find the general equation of a circle?

If the given circle is passing through two points, say A ( x 1, y 1) and B ( x 2, y 2), then these points must satisfy the general equation of a circle. Now put these two points in the given equation of a circle, i.e.: Also, the given straight line a x + b y + c 1 = 0 passes through the center ( – g, – f) of the circle.

How to find the value of (C) in the tangent?

As the tangent is a straight line, the equation of the tangent will be of the form (y = mx + c). We can use perpendicular gradients to find the value of (m), then use the values of (x) and (y) to find the value of (c) in the equation.