What does it mean for a circle to be tangent to the x-axis?
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What does it mean for a circle to be tangent to the x-axis?
If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point. The center of the circle must be equidistant from any of the points on the circumference. This means that both (0,3) and (3,0) are the same distance from the center.
What is the radius if the circle is tangent to the y-axis?
Because the circle is tangent to the y-axis, then the radius is 6 because it’s the distance from the center to the y-axis.
What does tangent mean in a circle?
A tangent to a circle is a straight line which touches the circle at only one point. The tangent to a circle is perpendicular to the radius at the point of tangency.
How to find the tangent of a circle to the Y-axis?
The equation for a circle is (x −h)2 + (y −k)2 = r2, where (h,k) is the center and r is the radius. Since you want the circle to be tangent to the y -axis, and we know that tangent refers to a line that touches something at exactly one point, we want the circle to have a radius that will make it just big enough to reach the y -axis.
What is the ⊥ – distance from (3 – 7) to the tangent line?
Indeed, the center is at (3, −7) and it touches the y -axis at exactly one point: (0, − 7). x2 +y2 − 6x +14y + 49 = 0. The reqd. circle touches the Y − Axis. Centre to the tangent line equals radius r. Now, the ⊥ − distance from (3, −7) to the Y − Axis, is |3|.
How to find the tangent of a circle using perpendicular gradients?
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\\). 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.
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.