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What is the point of contact when the line y equals 2x meets the circle x2 plus y2 -8x -y plus 5 equals 0?
Wiki User
∙ 6y ago
If: y = 2x
Then: y^2 = 4x^2
If: x^2 +y^2 -8x -y +5 = 0
Then: x^2 +4x^2 -8x -2x +5 = 0
Transposing terms: 5x^2 -10x +5 = 0
Dividing all terms by 5: x^2 -2x +1 = 0
Factorizing the above: (x-1)(x-1) = 0 meaning x = 1
By substitution into original equations point of contact is made at: (1, 2)
Wiki User
∙ 6y ago
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What is the difference between a point and a polygon?
A point and most of the time meets, a polygon is a circle thing that meets at some point!
Triangle pqr is an isosceles triangle in which pq equals pr equals 5cm it is circumscribed about a circle prove that qr is bisected at point of contact?
Suppose the circle meets QR at A, RP at B and PQ at C. PQ = PR (given) so PC + CQ = PB + BR. But PC and PB are tangents to the circle from point P, so PC = PB. Therefore CQ = BR Now CQ and AQ are tangents to the circle from point Q, so CQ = AQ and BR and AR are tangents to the circle from point R, so BR = AR Therefore AQ = AR, that is, A is the midpoint of QR.
What is the point of contact between the line y equals x plus 4 and the circle x2 plus y2 -8x plus 4y equals 30?
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 It appears that the given line is a tangent line to the given circle and the point of contact works out as (-1, 3)
True or false thee point which a tangent line meets a circle is called point of tangency?
True
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 point of contact when the tangent line y -3x -5 equals 0 meets the circle x2 plus y2 -2x plus 4y -5 equals 0?
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What is the difference between a point and a polygon?
A point and most of the time meets, a polygon is a circle thing that meets at some point!
The point at which a tangent line meets a circle is called the point of tangency?
true
Triangle pqr is an isosceles triangle in which pq equals pr equals 5cm it is circumscribed about a circle prove that qr is bisected at point of contact?
Suppose the circle meets QR at A, RP at B and PQ at C. PQ = PR (given) so PC + CQ = PB + BR. But PC and PB are tangents to the circle from point P, so PC = PB. Therefore CQ = BR Now CQ and AQ are tangents to the circle from point Q, so CQ = AQ and BR and AR are tangents to the circle from point R, so BR = AR Therefore AQ = AR, that is, A is the midpoint of QR.
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
What is the point of contact between the line y equals x plus 4 and the circle x2 plus y2 -8x plus 4y equals 30?
Equations: y = x+4 and x^2 +y^2 -8x +4y = 30 It appears that the given line is a tangent line to the given circle and the point of contact works out as (-1, 3)
What is the place where a tangent line intersects a circle?
Definition: a tangent is a line that intersects a circle at exactly one point, the point of intersection is the point of contact or the point of tangency. a tangent is a line that intersects a circle at exactly one point, the point of intersection is the (point of contact) or the **point of tangency**.
True or false thee point which a tangent line meets a circle is called point of tangency?
True
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 point of contact when y equals 5x meets y equals 3 -x on the Cartesian plane showing work?
If: y = 5x and y = 3 -x Then: 5x = 3 -x => 5x +x = 3 => 6x = 3 => x = 1/2 By substitution point of contact is at: (1/2, 5/2)
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 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.
