*5. Prove that no two lines in hyperbolic geometry are equidistant from one another by showing that the distance from one line to another cannot have the same value in more than two places.

Q: -z Q2. In the circle |z| = 1, Find the upper bound for 9z4+3z²+2l

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Q: 5. Prove that whole length of the curve x3 + y2/3 = a/3 is 6a.

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A: Let's find.

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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A: Find equation of locus :

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Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: The curvature of any line with slope m in 2-space at any point on it is TTL

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Q: 1) The maximum distance from the origin of the xy plane to the circle described by (x – 12)? + (y –…

A: given equation of circlex-122+y-62=16 As per our guideline we supposed to answer only first question…

Q: Demonstrate that the circles (x- 2)² + y² = 2 and x? + (y – 2)? = 2 share tangent at point (1,1),…

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Q: What is the length of the graph of y = In(x<+1) - x from x = 0 to x = 3?

A: Given  The graph equation is y=lnx2+1-x  from  x=0 to x= 3 .   Formula :- Arc length of curve…

Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

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Q: 6 of 19 Write the equation of a circle with centre (-8,-3) which is tangent to the x-axis. O (x –…

A: A detailed solution is given below

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

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Q: There are infinitely many secant lines from an exterior point to a circle. True or False? O True…

A: From a point outside the circle, infinite secants can be drawn to the circle

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Q: Suppose that line L does not intersect the circle centered at O having radius R. From O, drop a…

A: Closed point between two curves is length of common norm between them.

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Q: Demonstrate that the circles (x – 2)? + y² = 2 and x? + (y – 2)2 = 2 share tangent at point (1, 1),…

A: Here we will apply the concept of finding the equation of tangent to the two circles at point (1,1).

Q: 6. Show that the line with equation y = 3x – 5 is a tangent to the circle with equation x² +y? + 2x…

A: Equation of line : y=3x-5 Equation of circle : x2 + y2 +2x -4y -5=0 We have to prove that the line…

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

A: The functionals with in the calculus of variations are of the form V[f(x)]=∫abF(x,y(x),y'(x))dx The…

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Q: If z = x + iy, then the inequality |z + il < 3 is a: A. Circle with center at (0,1) and radius 3. B.…

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Q: In Pi Jinxing's dream, two curves are said to be CoRoNaViRaL if whenever they intersect, the two…

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Q: The tangent to the circle x2 +y2 +10 x+5 y= 60 at the point (2 ,4) is Select one: O None O 13 y +…

A: Given that:x2+y2+10x+5y=60

Q: Find the length of the tangent to the circle x²+y²-2x-3y-1=0 from the point (2,5).

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

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Q: 2. Let be the part of the circle x² + y² = 9 from (-3,0) to (0, 3) in the upper left quadrant.…

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Q: Find the shortest distance from the point (4,2) to the curve x^2 Зу^2 %3D 12 +

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Q: b. the length of the tangents from the point (2, 5) to the circle x +y² -14x-2y+34= 0

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

A: we have to find the radius of the circle

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Q: The DE for the family of circles of radius 9 is: A [1+ (y')²]³– 81=0 B [1+ (y')²]²- (» )²-[1+…

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Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

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Q: The curvature of any line with slope m in 2-space at any point on it is 0

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Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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Q: By using the calculus of variations, prove that the shortest distance between two points in the y z…

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.