0
What is the length of the tangent line from the point 8 2 to a point where it meets the circle x2 plus y2 -4x -8y -5 equals 0?
Wiki User
∙ 6y ago
Equation of circle: x^2 +y^2 -4x -8y -5 = 0
Completing the squares: (x-2)^2 +(y-4)^2 = 25 which is radius squared
Center of circle: (2, 4)
Tangent line originates from: (8, 2)
Distance from (8, 2) to (2, 4) is sq rt of 40 which is hypotenuse of right angle triangle
Using Pythagoras theorem: distance^2 minus radius^2 = 15
Therefore length of tangent line is the square root of 15
Wiki User
∙ 6y ago
Add your answer:
Earn +20 pts
What is the length of the tangent line from the point 9 0 to the circle x2 plus 8x plus y2 -9 equals 0?
Equation of circle: x^2 +8x +y^2 -9 = 0 Completing the square: (x+4)^2 +y^2 = 25 Radius of circle: 5 Center of circle: (-4, 0) Distance from (9, 0) to (-4, 0) = 13 which is the hypotenuse of a right angle triangle Using Pythagoras: 13^2 -5^2 = 144 and its square root is 12 Therefore the length of the tangent line is 12 units Note that the tangent line of a circle meets the radius of the circle at right angles
Difference between secant lines and tangent lines?
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
What is the term for a line that meets a circle or arc at only one point on it's exterior so it will not go through the circle?
a tangent to the circle
What line meets the circle at exactly one point?
The tangent line. A secant line hits the circle in two places and forms a cord, but the tangent line only hits the circle in one point and is always perpendicular to the radius of the circle which exists at that point.
True or false thee point which a tangent line meets a circle is called point of tangency?
True
What is the Radius tangent theorem?
The tangent of a circle always meets the radius of a circle at right angles.
What happens where a radius meets the tangent?
The radius and the tangent are perpendicular at the point on the circle where they meet.
What is an Angle whose side is tangent to a circle called?
There is no specific name for such an angle.
The point at which a tangent line meets a circle is called the point of tangency?
true
What is the length of the tangent line from the point 9 0 to the circle x2 plus 8x plus y2 -9 equals 0?
Equation of circle: x^2 +8x +y^2 -9 = 0 Completing the square: (x+4)^2 +y^2 = 25 Radius of circle: 5 Center of circle: (-4, 0) Distance from (9, 0) to (-4, 0) = 13 which is the hypotenuse of a right angle triangle Using Pythagoras: 13^2 -5^2 = 144 and its square root is 12 Therefore the length of the tangent line is 12 units Note that the tangent line of a circle meets the radius of the circle at right angles
Does a trigonometry tangent relate to a circle's tangent?
A circle's tangent is exactly the same as a triangle's tangent. If you look at a circle, you can make the radius the hypotenuse. Then make a vertical line from the point, and a horizontal line from the center. If you look, you have a triangle made inside the circle. This is why angles can be measured in radians, a unit that is derived from the circumference of a circle.-------------------------------------------------------------------------------------------By doing a little calculus, we find that the slope of the equation of a circle-the slope of the tangent line-is given by the tangent of an angle.AnswerEverything written above is correct, but doesn't have anything to do with tangents (in the circle sense of the word). Suppose you're given an angle theta. Draw a circle together with two radii, one horizontal and the other at an angle theta from the first one. (So far, this is the same as above.) Now draw the tangent to the circle at X, the point where the non-horizontal radius meets the circumference. Let Y be the point where this tangent meets the horizontal line through the centre. Then, assuming the radius is 1, tan(theta) is the distance XY, which is the length of part of the tangent.
Difference between secant lines and tangent lines?
A secant line touches a circle at two points. On the other hand a tangent line meets a circle at one point.
What is the term for a line that meets a circle or arc at only one point on it's exterior so it will not go through the circle?
a tangent to the circle
What is the length of the tangent line from the point 9 0 to a point where it touches the circle of x2 plus 8x plus y2 -9 equals 0?
Equation of circle: x^2 +8x +y^2 -9 = 0 Completing the square: (x+4)^2 +y^2 = 25 Radius of circle: 5 Center of circle: (-4, 0) Distance from (9, 0) to (-4, 0) is 13 which is the hypotenuse of a right angle triangle Using Pythagoras' theorem: 13^2 -5^2 = 144 and its square root is 12 Therefore length of tangent line is: 12 units Note that a tangent line always meets the radius of a circle at right angles.
What is the point of contact when the tangent line y -3x -5 equals 0 meets the circle x2 plus y2 -2x plus 4y -5 equals 0?
It works out that the tangent line of y -3x -5 = 0 makes contact with the circle of x^2 + y^2 -2x +4y -5 = 0 at (-2, -1)
What line meets the circle at exactly one point?
The tangent line. A secant line hits the circle in two places and forms a cord, but the tangent line only hits the circle in one point and is always perpendicular to the radius of the circle which exists at that point.
What line on a circle only intercepts once?
tangant of circle intercepts it only on one point. In real the point where tangent meets the circle and intercepts it are same
