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What is the tangent line equation of the circle x2 plus y2 -6x plus 4y -7 equals 0 passing through the point 1 2?
Differentiate the circle equation to find the slope at any given point.
x^2 + y^2 -6x + 4y -7 = 0
2x + 2y(dy/dx) - 6 + 4dy/dx =0
2x - 6 + (2y + 4) dy/dx =0
dy/dx = (6 - 2x) / (2y + +4)
At the point ( 1,2)
dy/dx = (6 - 2(1)) / (2(2) + 4)
dy/dx = 3 / 8 The slope /gradient of the tangent line.
At the point ( 1,2)
y - 2 = (3/8)(x - 1)
y - 2 = 3x/8 - 3/8
y = 3x/8 + 13/8
or
8y = 3x + 13
or
8y - 3x = 13
or
8y - 3x - 13 = 0
8
What else can I help you with?
Does a tangent circle pass through the center of the circle?
If the tangent circles are outside of one another, then neither passes through the center of the other. If one circle is within the other, then the inner tangent circle might contain the center point of the larger circle. There will be infinitely many inner tangent circles that do not.
How do you construct a line tangent through a circle through a point outside the circle?
The tangent line only touches the outside of a circle at one given point. So an outside line perpendicular to the circle's diameter at 90 degrees should do.
What do you call a line that passess through a circle at exactly one point?
The diameter of a circle passes through the center of a circle at its center point
How many tangents can be drawn to a circle containing a point inside a circle?
No tangent No tangent
How many lines can be drawn through a given point on a circle that is tangent to the circle?
Infinite lines because a circle has infinite lines of symmetry.
What is a chord passing through the center of a circle?
a diameter
What is the equation of the tangent line that touches the circle x squared plus y squared -8x -16y -209 equals 0 at a coordinate of 21 and 8?
Circle equation: x^2 +y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius of circle 17 Slope of radius: 0 Perpendicular tangent slope: 0 Tangent point of contact: (21, 8) Tangent equation: x = 21 passing through (21, 0)
A secant tangent passes through the center of a circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
What is the tangent equation of the circle x2 plus 6 plus y2 -10 equals 0 when it passes through 0 0 on the Cartesian plane?
Circle passing through coordinate: (0, 0) Circle equation: x^2 +6 +y^2 -10 = 0 Completing the squares: (x+3)^2 +(y-5)^2 = 34 Centre of circle: (-3, 5) Slope of radius: -5/3 Slope of tangent: 3/5 Tangent equation: y-0 = 3/5(x-0) => y = 3/5x
Does a secant tangent angle pass through the center of the circle?
Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
What is the equation of the tangent line that touches the circle x squared plus y squared -8x -16y -209 equals 0 at the point of 21 and 8?
Circle equation: x^2 +y^2 -8x -16y -209 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius: 17 Slope of radius: 0 Tangent equation line: x = 21 passing through (21, 0)
What is the equation for a circle with its center at the origin and a tangent whose equation is y equals 7?
x2 + y2 = 49
A tangent circle passes always through the center of the circle?
A line joining the centres of two tangent circles also passes through the point of tangency.
Does always a tangent to a circle pass through the center of the circle?
the tangent will never go through the center of a cirlce. The tangent is, by definition, a line that only intersects the circle at one point. If you look down a pencil along its long axis, so that it appears to be a circle, and place your finger on top of and perpendicular to the pencil, your finger is now tangent to the circle you see.
The center of a circle is located at c(3-13). The x-axis is tangent to the circle at (30). Find the equation of the circle?
Equation of the circle: (x-3)^2 +( y+13)^2 = 169
How is a tangent different from a chord?
A Tangent is a straight line, outside the circle, that just touches the circle circumference in one place. A Chord is a straight line , inside the circle, but not passing throught the centre. and touches the circle circumference in two place.
What is a tangent line with respect to a circle?
A tangent to a circle is a line which touches the circle once. That is, it does not pass through the circle, which would mean intersecting it twice. A way to form a tangent is draw any line from the centre point of a circle to its edge. A line on the edge perpendicular (at 90 degrees to) this line will be a tangent.
