true or false?  The circle with center at the origin and radius of 1 has equation x^2-y^2=1

Q: Find the shaded area of diagram that shecked by curve y = x2 + 2x and the line y = -x.

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Q: The exact value of the curvature of ƒ(x)=arcsin x when x= , can be expressed as the product of a/b…

A: Given,               f(x)= arcsin xDifferentiating both sides with respect to x…

Q: Describe a surface of revolution in your own words.

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Q: Describe how to determine and find the equation of a circle with center on the line y = 0.5x + 3…

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Q: Draw a diagram to show that there are two tangent lines to the parabola of y = x2 that pass through…

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Q: How do you find a tangent line of a circle Equation: (x - 3)2 + (y - 5)2 = 5 Point: (4,7)

A: solution:- Given                x-32+y-52=5                 point  4,7The above lies on the…

Q: What is the equation of the tangent line to the circle x2 + y? = 34 at the point (5, 3)?

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Q: A circle with radius 5 has its center at origin. What is the equation of the tangent line to the…

A: The equation of a circle centered at and has a radius r is defined by the equation, . The slope of…

Q: I need help with writing a parameterization for the curves in the xy-plane. A circle of radius 4…

A: Write in parametric form

Q: Among the following, what is the center of 2 circles tangent to x^2+y^2=100 at (6,-8) with a radius…

A: the radius of circles is given as 15 units tangent is passing through point (6, -8)

Q: Two circles of radius 4 are tangent to the graph of y = 4x at the point (1, 2). Find equations of…

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Q: A point starts at (x, y) = (6,0) and moves CCW along a circular path centered at (x, y) = (0, 0).…

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Q: Find an equation of the cricle that satisfies the given conditions. (Use variable x and y.) Circle…

A: It is given that both x and y-axes are tangent to the circle and circle has the radius 4 with the…

Q: a. Circle of radius 1 and centers on the line y = x

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Q: How to find an equation of the line tangent to the circle x^2+y^2-6x-2y-15=0 at the point (6,5) ?

A: Note:- The standard form of equation of tangent line at point c, d is y-d = m x-c Here, m is the…

Q: A circle is tangent to the line 2x-y+1=0 at the point (3,5) and the center is on the x+y=9. Find the…

A: Given that equation of tangent to the circle is  2x-y+1=0 at point (3,5)

Q: Find the points where the line y=x4 intersects a circle of radius 2 centered at the origin. Give…

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Q: At what point in the first quadrant does the line with equation y = 1.5x +3 intersect the circle…

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Q: Find the area of the ellipse x^2+14 x y+245 y^2=4 by using a suitable transformation that maps to…

A: Given equation is, x2+14xy+245y2=4 The equation can be written as,…

Q: Find the points where the line y=−3xy=-3x intersects a circle of radius 2 centered at the origin.…

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Q: 17. Explain the distinguishing feature of the distance between the foci and a point on the eilipse.

A: Here we need to determine the distinguishing feature of distance between the foci and a point on the…

Q: 375m. With a 160m lon

A: Two tangents intersect at Sta 12+200km with a descending grade of 6% and an ascending grade of 2%…

Q: Look up the curves called hypocycloid and epicycloid. Writea report on what you find. Be sure to…

A: An epicycloid is a plane curve created by tracing a chosen point on the edge of a circle of radius r…

Q: Find a path that traces the circle in the plane y = 3 with radiusr = 5 and center (0, –3, 2) with…

A: the plane y = -3 with radius r = 5 and center (0, -3,2) with constant speed 20 To determine a path…

Q: Draw a diagram to show that there are two tangent lines to the parabola y = x² that pass through the…

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Q: What equation is tangent to the circle (x-4)² + (y- 2)* = 25 at the point (8,5)?

A: concepts remember for this question are; 1. The general equation of a straight line is y = mx + c,…

Q: hat is the families of the curve of all circles with fixed radius r and tangent to the x-axis

A: Given           Radius of circles =r      and all circles are tangent to the x-axis.…

Q: Find the coordinates of the point at -50° on a circle of radius 4.7 centered at the origin.

A: x=r cos θ , y=r sin θr is the radius, θ=-50°

Q: What equation is tangent to the circle (x-4)^2 + (y-2)^2=25 at the point (8,5)?

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Q: Find the points where the line y=−x/4 intersects a circle of radius 8 centered at the origin. Give…

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Q: Circles with fixed radius r and tangent to the x-axis.

A: The general equation of the circle with center (h, k) and radius r is given by  (x-h)2+(y-k)2=r2

Q: 1) What is the equation of 5 center the circle whose center is (4, 2) (4, 2) and is tangent to line…

A: Given the center of the circle is (4,2) and is tangent to line y=-5. Since, the tangent is a line…

Q: The curvature of a circle of radius 2

A: Note that a circle of radius r has the curvature of 1r.

Q: Find equations of the lines passing through the origin that are tangent to a circle with radius 2…

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Q: A circle centered at (9, 15) has only 1 y-intercept. What is it's radius?

A: Given : Center of Circle is (9 , 15) has only 1 y-intersept. To find : Radius of circle  Solution :…

Q: Sketch the curve y cu. = x sq.

A: Given the curve is y3 = x2 Put random value in the curve and we get the table which help to trace…

Q: Find the equation of line tangent the circle x ^ 2 + y ^ 2 = 25 at point at (3, - 4)

A: Differentiate the equation and get slope of tangent at (3,-4) ddxx2+y2=ddx252×3+2×-4×dydx=0dydx=34

Q: Cannot solve

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Q: Tangents are drawn to the concentric circles x^(2)+y^(2)=a^(2) and x^(2)+y^(2)=b^(2) at right angle…

A: We have to Show that locus of their point of intersection is a 3rd concentric circle and find its…

Q: Find the point in the first quadrant where the line y=2x intersects a circle of radius 3 centered at…

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Q: ind an equation of the circle with centre C(3,-2) and tangent line y=5 .

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Q: Give the equation of a circle tangent to the line 3x + y -2 = 0 at (-1, 5) and with a radius equal…

A: Topic = Circle

Q: Consider a circle with center at the origin and with radius 3. a What is the equation of the circle…

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Q: Find the length of the arc of the curve from point P to point Q. y - , (-3, 3), (3, %).

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Q: Find an equation for the line tangent (in general form) to the circle at point (4,-3). The circle…

A: For the figure  given below: Equation of a tangent to a circle at point (a,b)  with radius r and…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)^2=2y, the…

A: Solution of the problem as follows

Q: the shaded area shown in the figure is bounded by the line with equation y = 12-7x-x² and the line…

A: given functions are                                              y=12-7x-x2, y=4…

Q: .3 The curve y3Dx+ x*-x has two horizontal tangents. Find the distance between these two horizontal…

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Q: What is the families of the curve of all circles with fixed radius tangent to the line x=4

A: Given: Families of the curve of all circles with fixed radius and tangent to the line x=4 Let h, k…

Q: 4. Find the equation of the circle that is tangent to the line x = 8 that has a center at (-5, 10).

A: The general equation of circle having the center at h,k and radius r is given as, x-h2+y-k2=r2 it is…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.