The general form of an equation of a circle is (x – h)2 + ( y – k)2 = r2. If we solve the equation for x we get equations of the form x = h ± V² – (v – k)?: The equation x = h + Vr² – (v – k)? represents the graph of the Vr? – (v – k)² represents the graph of the left-side semicircle. Likewise, if we solve for y, we have y = k + V? – (x – h)?. These equations represent the top and corresponding right-side semicircle, and the equation x = h – bottom semicircles. For Exercise, graph the equations. a. y = V9 – x² b. y = - V9 –x %3D C.x = V9 – y d. x = -V9 – y %3D

Q: 6. If x(t) = e' +1 and y=2e²ª are the equations of the path of a particle moving in the xy-plane,…

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A: We have to find the radius

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A: Given: 9x2+25y2-144x +200y + 751=0

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A: Solution is done in step 2

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A: Solution:-

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A: Solution:-

Q: (b) Sketch the graph of the function y = 1+ /16 – x²2 for -4 < x < 4. Hint: x2 + y? = 16 is the…

A: Consider the equation of the circle The graph can be plotted for the circle as

Q: Find the points on the curve x^2y = 2 nearest the origin.

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A: The graph is compressed by the factor of 12 therefore New Value of X=12x 2X=x

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Q: Find the point (a, b) on the graph of y = e^x where the value ab is as small as possible.

A: Solution:Given y=exTo find(a,b)  where ab is as small as possible.

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Q: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

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Q: Given that 10x6 + 3x- x? f(x) : %D x2 a) Simplify f (x) b) Hence, or otherwise, find g(x) = | f(x)…

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Q: 2x +2y +4 + 8y + 2 = 0 is the equation of a circle with center (h, k) and radius r for: h and and

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Q: Match the equation with its graph. 2t r(t) = ti + In(t)j + k, 0.1 < t< 5 3

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A: We will solve the given equation in form of (x-h)2 + (y-k)2 = r2

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Q: The cartesian equation of the curve x = VE ,y = 1-t is: (a)y = 1-x2, x20 (b)y = 1-x ,x20 %3D (c) x =…

A: Cartesian equation is a equation which involves x and y , just I have eliminate the t from given…

Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y &gt; 0

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Q: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

A: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

Q: The cartesian equation of the curve x= f ,y = 1-t is : (a)y = 1– x², x 20 (b)y =1-x ,x 2 0 (c) x = 1…

A: The given curve is in paramatric form as following- x=√t y=1-t Where t is a parameter. To find the…

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A: The solution is given below

Q: Find the point on the graph y=Vx+1 that is closest to the point (2, 1).

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Q: The general equation of the circle that passes through the points (-3,4), (2,–6), and (5,0) is x2 +…

A: Given: Let us consider the given general equation of the circle, x2+y2+Dx+Ey+F=0 and the circle…

Q: 10. The radius of the circle with equation x² +y² – 10x + 12y + 41 = 0 is A 5V2 B 3V5 с 25 D 4V5

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Q: The equation x2 + y2 + Dx + Ey + F = 0 is called the_________ form of the equation of a circle.

A: The general form of the equation of a circle is x2+y2+Dx+Ey+F=0. D, E and F are constants.

Q: Find the equation of the curve for which y" = x, and which passes through the point (1, 2) with (A…

A: Given y'' = x  and the curve passes through (1,2)  with a slope of 5/2. which means y(1) =2, y'(1)…

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Q: Find the coordinates of the point in the curve y = 12x – 2y + 23 that is nearest to the point P(10,…

A: Given curve: y2=12x-2y+23 The point is  P10,4 To find: The coordinates of the point on the curve…

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A: topic - equation of tangent line to curve

Q: The length of the curve z=z(t)=5e", Ostsa is а) 12л b) л c) 157 d) 2

A: Sol :-                Are length in (a,b) if functions are                               x(t) , and…

Q: How far from the x-axis is the center of the curve 2x2 – 2y2 + 10x – 6y – 55 = 0?

A: The given equation of the curve is: 2x2 – 2y2 + 10x – 6y – 55 = 0 This can be written as:

Q: The equation of the circle whose center lies in the first quadrant on the straight line y=2x, passes…

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Q: A parabola has an equation of x² = 6y + 10. Compute the equation of a tangent to the curve which has…

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Q: Find the points on the curve x2y = 2 nearest the origin.

A: The curve is x2y=2 Let x1,y1 and x2,y2 be two points, distance betwwen these points is x2-x12+y2-y12