In geometry, it is known that the tangent line to a circle at a given point A on the circle is perpendicular to the radius drawn to point A. Suppose that line L is tangent to the given circle at the point (4, 3). Write an equation representing line L. A(4, 3)

Q: 1 Find the distance from the origin to the point P(2, 8, –4)

A: Given: P2,8,-4, Q0,0,0 We know that distanced between pointsx1,y1,z1,x2,y2,z2 is given by…

Q: Find all points on y-axis of the rectangular coordinate system that are a distance 6 from the point…

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Q: In the figure to the right, lines that appear to be tangent are tangent, and O is the center of the…

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Q: 2. How many common tangents can you draw for the pair of circles? Your answer

A: We can draw 4 tangents.

Q: Write an equation of the line passing through point P(3,8) that is parallel to the line y = (x + 4).…

A: Equation of the given line is y=15(x+4)   And the given point is P(3, 8).

Q: 5. Write an equation of the line tangent to the circle x? + y? = 29 at (5, 2).

A: Topic - tangent to the circle

Q: Find all points on the y-axis that are a distance 6 from P(5,3).

A: A point on the y axis is of the form (0,k) , where k= real number. Let (0,k) is 6 units away from…

Q: Find the slope of the line from the origin to the midpoint P of side AB in the triangle in the…

A: Given : A(a,0), B(0,b), O(0,0) Suppose the coordinate of P are (x,y)

Q: 15. Determine the coordinate of point C, which lies on the y-axis, if it is equidistant from point A…

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Q: Let a point a = (2, 4, 5). b) Find the distance from this point to the z-axis.

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Q: Find the curve in the ??-plane that has a slope at each point given by 1/?^3 and

A: Find the curve in the ??-plane that has a slope at each point given by 1/?^3 and passes through the…

Q: Find the slope of the line tangent to the graph of y = 2x – 2x + 57 at (–2, 45). 22 52 45

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Q: A circle with center C(4,-2) contains the point D(8,1). What is the equation of the line…

A: Given: The center of the circle is C4,-2 and contains the point D8,1 To find the equation of the…

Q: Which of the following is an equation of the line, in standard form, that passes through the points…

A: Use the two points form of equation of straight line.

Q: Find the distance between the two points shown below 3- B -5 -4 -3 -2 -1 3 4 5 6 -3- -4 A -5 -6-…

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Q: Write an equation of the line tangent to the given circle at the given point. (x + 7)2 + (y – 9)2 =…

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Q: The line that passes through point H has the equation y z +2. The equation of the line parallel to…

A: The solution is:

Q: Assume that lines that appear to be tangent are tangent. What is the value of x? C 8. 12 units. X =

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Q: Find equations of the lines that pass through the given point and are (a) parallel to and (b)…

A: We have to find the equation which is parallel to x-y=4 and passes through the point 2.5,6.8. Also…

Q: Find all points on the y-axis that are a distance 13 from P(12, 6).

A: To find: All the points on y-axis that are a distance 13 from P12,6. Concept used: The x-coordinates…

Q: There is a line, j(x), that passes through the point (1, 4) and is perpendicular to the line h(x) =…

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Q: Find an equation of the line that is tangent to the circle x? + y? = 25 at the point P(3, 4).

A: Given: Equation of circle: x2+y2=25 To find: Equation of line which is tangent to the circle at the…

Q: Find the value of x,if the distance between the pints (x,1) and (3,2) is 5

A: We have to find the value of x if the distance between the points x,1 and 3,2 is 5.

Q: Find the midpoint of the segment GH given: G(7, -5) and H(9, -1).

A: Given data: The first point given is G(x1, y1)=(7, -5). The second point given is H(x2, y2)=(9, -1).…

Q: Which of the following lines is perpendicular to a line with the equation: y

A: When two line intersect perpendicular then it's slope product is minus one.

Q: 1. Determine the equation of the circle which is tangent to the line 21y = 20x - 42. The center of…

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Q: Find an equation of the line that satisfies the given conditions. Through (8, 5);  parallel to the…

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Q: If f'(a)=, what is the slope of the line tangent to the graph of y = f(x) at the point (a, f(a))? O…

A: Given: the curve, y=fx.f'a=12

Q: 2) Given the circle x2 +y = 25 and point P (x,y,) on the circle, find the equation of the line in…

A: We have to find equation of line in slope- intercept form:

Q: Find a general form of an equation of the line through the point A that satisfies the given…

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Q: a.Find the exact distance between the points. b. Find the midpoint of the line segment whose…

A: to find the distance between (−1, 8) and (4, −2) we need the distance formulaAnswer: Exact distance…

Q: Find the exact length of the curve. X √(y - 3), 16 ≤ y ≤ 25

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Q: 4. Determine the equation of the line that has a distance 2 from the origin and is parallel to the…

A: equation of aline that passes through (2,7) and (-3,-2)…

Q: Providing a proper explanation, trace the curves: (1) a?a = y°(2a - y), where a > 0,

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Q: 19. Use similar triangles to show that the slope of the line through any two points on that line is…

A: We know slope = Difference in y- coordinatesDifference in x- coordinates Consider the figure in the…

Q: Find all points on the y-axis that are a distance 6 from P(5, 3).

A: P5, 3 is at a distance of 6 units from the y-axis

Q: Which of the points below correctly plots the point (2, 6.

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Q: The line parallel to y=?x+5, passing through the point (3, 2)

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Q: Write an equation of the line tangent to the given circle at the given point.  (x - 3)2 + (y + 2)2…

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Q: Given the pair of points: (0,-5) and (-1,6), a) Find the distance between the two points. b) Find…

A: The pair of points is (0,-5) and (-1,6).

Q: Write the general forms of the equations of the lines that pass through the point and are (a)…

A: Given: The equation of the line, x=1 and the point, -7,-2.

Q: A В Use the method above to find the distance from the point P(-3, 1,5) to the line through A(1,…

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Q: The line that passes through point H has the equation y = z+ 2. tion G The equation of the line…

A: Point G coordinates = (-3, 0)  Slope of perpendicular line = -1/m Here m is slope of given line.  So…

Q: 1. The midpoint of the line segment betw coordinate of P1. A. (6, -5) В. (5, -6)

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Q: Find a general form of an equation of the line through the point A that satisfies the given…

A: The general form of equation of line is  ax+by+c=0 . If we have the general form of equation of line…

Q: How many lines can be drawn from a point outside a circle that are tangent to the circle?   A)  0…

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Q: Create a cartesian equation of a line in R using the digits (6,-5,-4). o Find a NEW cartesian…

A: Given: Digits to be used to find the equation of a line in ℝ2 6,-5,-4 To find: Equation of a line…

Q: 4) Find the two points of the form (x,-4) that have the same distance of 10 units from the point…

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