The Greek method for finding the equation of the tangent line to a circle uses the fact that at any point on a circle the lines containing the center and thetangent line are perpendicular . Use this method to find an equation of the tangent line to the circle x2 + y2 = 9 at the point (1, 2√2).

Q: In the given image, ⊙P is centered at (10, −6) with the x-axis tangent to the circle at point T.…

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Q: A circle in the xy- plane has equation (x – 2)2 + (y + 5)2 = 36. %3D Which of the following points…

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Q: Find the equation of a circle centered at (1, −1) and tangent to the line 2x + 3y = 12

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Q: Find all points having an x-coordinate of 3 whose distance from the point (-2,1)is 13 (a) By using…

A: (a) By using the Pythagorean Theorem (see graph below)   Let (-2,1) denote the coordinates of the…

Q: Form the diffrential equation of the family of circle having a centre on y-axis and radius 3 units.

A: the objective is to find the differential equation of the family of circles having centre on y axis…

Q: In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the…

A: Let O be the center of the given circle. Suppose the tangent at P meets BC at Q The join BP. The aim…

Q: The circles defined by the equations (x + 3)2 + (y- 2)2 20 and (x +3)2 + (y - 2)2 = 45 have the same…

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Q: A В C 3X +4 5X - 6

A: B is the midpoint of AC⇒ AB=BC

Q: Determine whether line segment AB is tangent to the circle. If yes, choose the equation that proves…

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Q: Use the arc length formula to find the length of the curve y = 7- 4x, -1sxs 3. Check your answer by…

A: It is known that arc length of any curve is given by the integral, We have,

Q: Find the equation of the circle that passes through the point (9,7) and is tangent to both the y…

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Q: The equation of a family of circles with center (2,k) and radius r that is tangent to the x-axis is?

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Q: Find the point (x, y) on the unit circle that corresponds to the real number t. t = 3π/2     (x, y)…

A: Given that

Q: when the center of a circle is at the origin, the equation to be used is when the center of a circle…

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Q: I need a paragraph proof for proving that a circle and a line cannot intersect in three or more…

A: The equation of line is y = mx + c and the general equation of circle is (x – a)2 + (y – b)2 = r2…

Q: he circle is tangent to the y-axis and the center is at (-2,-8).

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Q: . Find the exact coordinates of a point corresponding to 4pi/3 on a circle radius 10.

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Q: Consider the two points (4, –3) and (5, 7). The distance between them is: The x co-ordinate of the…

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Q: Find the exact length of the tangent to the circle with equ a? + 8x + y? – 6y + 16 = 0 from the…

A: Topic:- Geometry

Q: If a focal chord of y =16x is a tangent to the circle (x-6)° +y² = 2, then the positive value of the…

A: Introduction :__

Q: Suppose you are given equations of two overlapping circles as a. Determine how to find the points of…

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Q: b) What goes wrong if you try to apply the same procedure to find all the points on the circle r? +…

A: Given,                  x2+y2=3      We know that,      To find all rational points on the…

Q: Find the value of  x for which the distance between the point P(2, -3) and Q (x, 5) is 10

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Q: b) Show more generally that the lines joining any point on a circle to the endpoints of a given…

A: To show - Show more generally that the lines joining any point on a circle to the endpoints of a…

Q: ind the equation of the circle that pass through the intersection of the circles x2 +y2 +2x +4y-4=0…

A: Here we have to find the equation of the circle that passes through the intersection of the circles…

Q: Determine if AB is tangent to the circle. 12 6.

A: In the question it is asked to proof that line segment AB is tangent to the given circle.

Q: Find all points having a y-coordinate of -6 whose distance from the point(1,2) is 17. (a) By using…

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: 2. Find points P and Q on the parabola y = 1 – x? so that the triangle ABC formed by the r-axis and…

A: Given:  To find points P and Q on the parabola y=1-x2 so that the triangle ABC formed by the x‐axis…

Q: What are the coordinates of point P on the unit circle U if the real number t = (-15π/2)?

A: We have to find coordinate point P on the unit circle for t=-15π2

Q: 4. Write the equation for a circle tangent to the y-axis and with center (5, 6). It may be helpful…

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Q: 6. In the accompanying diagram, PQ is tangent to circle O at Q and PRT is a secant. If mZP - 56 and…

A: To find : m arc QR

Q: Concentric with the circle x ^ 2 + y ^ 2 - 4x + 6y - 17 = 0 and 3x - 4y + 7 = 0 equation of the…

A: Solution:- x2+y2-4x+6y-17=0 x2-4x+6y+y2=17 x2-4x+4+6y+y2+9=17+4+9 x-22+y+32=30 Center of circle (2,…

Q: Which of the points (x, y) does NOT lie on the unit circle?

A: We have given four points and we have to check among these four points which points are not lie on…

Q: The coordinates of the points A and B are (-2, 3) and (4,1), respectively. An equation of the circle…

A: Please consider the handwritten solution.

Q: Among all triangles in the first quadrant formed by the x-axis, the y-axis, and tangent lines to the…

A: First of all, consider function y given.Plot the graph for the function y.The triangle can be formed…

Q: 7. Show that: x² + 8x + y2 – 10y - 8 = 0 is the equation of a circle. What is the center of this…

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Q: If the radius of the circle x2+y2-8x+10y+k=0 is 9. Then find the value of K

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Q: What are the four main end points to the circle x2+y2-10x+8y+25=0 (show work)

A: Question is solved.

Q: The side length of this square is x. What is the ro of the circle?

A: The length of the side of a square is x units.

Q: Use the arc length formula to find the length of the curve y = 4x – 5, -1 < x < 3. Check your answer…

A: The arc length of the function y(x) over the interval a ≤x≤b is determined by the formula,

Q: A mosque has a "keyhole" entry consisting of a rectangle surmounted by a circle. The two opposite…

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Q: If the abscissae of points A, B are the roots of the equation x² + 2ax − b² = 0 and ordinates of A,…

A: If the abscissae of points ,A,B are the roots of the equation x2+2ax-b2=0and ordinates of A,B are…

Q: Consider the two points (4,2) and (10,4). The distance between them is:   The x co-ordinate of the…

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Q: At what points will the line y =x intersect the unit circle x2 +y2 =1 ?

A: We have to find the points where line y=x is intersecting the unit circle: x2+y2=1 To find the…

Q: At what points will the line y = -2x intersect the unit circle x2 +y2 =1 ?

A: The circle equation is x2+y2=1 and the line equation is y=-2x.

Q: Find the angle formed by the li 3x+4v-12=0 with the x-axis.

A: The slope of a line: The change in y-coordinate with respect to the change in x-coordinate of a line…

Q: Find the point (x, y) on the unit circle that corresponds to the real number t. t= π/2 (х, у) -

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Q: The equation of a circle centered at (0, 8) with a radius of is given by which of the following…

A: Given: Center (0,8) and radius =√30

Q: The equation of a circle is given as x2+ax+y2+by=c where a, b, and c are constants. The radius of…

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Q: 2. Find the equation (in general form) of the tangent lines to the circle x² + y² - 8x + 10y = 128…

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