2. Find points P and Q on the parabola y = 1 – x? so that the triangle ABC formed by the r-axis and the tangent lines at P and Q is an equilateral triangle (see figure 1).

Q: 1+ 1 А 3. Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the…

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Q: In the figure below, AB is tangent to circle O at point A, secant BD intersects circle O at points C…

A: We have to find the angle

Q: Evaluate (x + y?) dx + 3x dy, where C consists of the arc of the parabola = y? from (1, 1) to (4,…

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Q: 2x +3K Zx2 - 4x + 13

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Q: Find a formula for the distance from the point P(x, y, z) to the y-axis.

A: Given : The point is P ( x , y , z ) to the y - axis .

Q: Find the equations of the tangent line in the given plane. Tangent to the parabola z = x? + 3y2 , x…

A: Topic- application of derivatives in 3-D

Q: Find the lengths of the curves The parabolic segment r = 6/(1 + cos θ), 0 ≤ θ ≤ π/2

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Q: 3. Which point of the unit circle of y = sin x has is A. -1 B. ± 1 С. 1 D. 0

A: To find a unit circle of y=sin x has its highest value

Q: Find the curvature k of the circle C : (x – 2)² + (y + 3)² - at the point (5, 1).

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Q: In the figure below, VY and VW are tangent to the circle centered at O. The segment YW passes…

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Q: BG and BH are tangents that intersect circle M at points G and H, then A. MZGMH = 120° B. BG = BH C.…

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Q: Show that if P lies on the intersection of the two curves x2 - y2 = c and xy = d (c, d constants),…

A: Given : The two curves x2 - y2 = c and xy = d intersect at point P where c and d are constants.…

Q: Show that if P lies on the intersection of the two curves x2 − y2 = c and xy = d (c, d constants),…

A: Solution:Givenx2-y2=c     and   xy=dTo prove tangent curve at P are…

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: In the given figure , the common tangents AB and CD to two circles with centres O and O' intersect…

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Q: Find points P and Q on the parabola y = 1 – x² so that the triangle ABC formed by the x- axis and…

A: We have △ABC is an isosceles right angle triangle. So the interior angle at B and C must be 45° The…

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: Find the points on the curve 5x + 5y? - 6xy - 6xy = 4 nearest to the origin.

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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…

Q: Prove that the locus of the point of intersection of two tangents to the parabola y? = 4ax, which…

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Q: 9. Find the curvature, radius of curvature, and the equation of the circle of curvature at the point…

A: Given  y=2x3+3x2-12x-2936 To find Radius of curvature, curvature & The equation of circle of…

Q: a. Find the length of the arc of the semicubical parabola ay=x' , from x= to x= 5a.

A: Arc length of the curve

Q: To find the points on the cone z? = x² + y² that are closest to the point (5,2,0) , we need to solve…

A: Given  z2=x2+y2 let the P (5,2,0) and P (x,y,z) so, d = x-52+y-22+z-02 d=x-52+y-22+z2d=…

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: In the figure on the right, xy and xz are tangents from an external point X. 1. Is XY congruent to…

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Q: Find the curvature k of the circle C:(x – 2)2 + (y +3) = 25 - at the point (5, 1).

A: circle equation is x-22+y+32=25 and point 5,1find curvature k

Q: BC is a tangent drawn to circle O. OC = 16, BM = 10. Find BC to %3D the nearest tenth. C B to M 16

A: Given: -  BC is a tangent drawn to circle O. OC = 16, BM = 10. To Find BC

Q: Suppose the angle formed by the line y = 4x and the positive x-axis is 0. Find the tangent of 0. %3D…

A: The objective of the question is to find the tangent of angle that is formed by the line y=4x and x…

Q: A wire ACB passes through a ring at C, which is attached to a sphere rotating at constant speed v in…

A: Given data   and  v=8 ft/s Apply equilibrium equation ,

Q: In AWXY, the measure of ZY=90°, XW = 53, YX = 28, and WY = 45. What is the %3D value of the cosine…

A: I am going to solve the given problem by using some simple geometry to get the required result.

Q: 8. Show that the circle and the ellipse are tangent to each other and draw the figure, x? + y? – 6x…

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Q: The circles r (V3/2, 7/3). Show that their tangents are perpendicular there. V3 cos 0 and r = sin 0…

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Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: The points P(ap2 , 2ap) and Q(aq2 , 2aq) lie on the parabola y2= 4ax. Prove that if PQ is a focal…

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Q: If a parabola defined by f(x)=2−x^2 is inscribed under an equilateral triangle ABC, so that the…

A: Given data:     The given equation of parabola is: f(x)=2-x2.     The below figure represents the…

Q: Find the equation of a circle whose center is at (3, -5) and whose radius is 4. A. x² + y? – 6x +…

A: Use general equation of circle:  (x-x0)^2 + (y-y0)^2 = r^2  And equation of parabola is : (y-y0)^2 =…

Q: Evaluate x° ds where C is the part of the parabola y = x² from (0,0) to (2, 4).

A: Form the double integral and set the limits than integrate with respect to y and x.

Q: 1. In the example above, what is the height of the tunnel 12 ft away from the center towards the…

A: From the  example above,                                      We can see that we are using the…

Q: Evaluate (x - iy) dz along (a) the parabola y = 2r? from (1, 2) to (2, 8),

A: In the given problem we have to evaluate  ∫C(x2-iy2)dz  along the parabola  y=2x2 from (1,2) to (2,…

Q: 8. PT is tangent to circle O at P If mNP = 90°, and mMXP : 186°, find %3D %3D X/ d. mZ4 e. mZ5 f.…

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Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: In R', the equation x² + y + z? = 4 describes a sphere of radius 2. Select one: True O False

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Q: Find the curvature K of the circle C: (x - 2) + (y+3)² = 16 %3D at the point (2, 1).

A: Given: Equation of circle C: (x-2)2+(y+3)2=16 ⇒ (x-2)2+(y-(-3))2=42 We know that circle equation is…

Q: The tangent and the normal to the parabola y²=20x at the point T(5,10) meet the x-axis at the points…

A: Details solution is given below:

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 4? a = b…

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Q: a) Because point Q is their common R V center, these circles are known as (W circles. b) If RQ the…

A: a) We know that the circle having same center but different radii are called as concentric circle.…

Q: If C1 is the segment connecting (x1, Y1) to (x2, Y2), find | x dy – y dx in terms of the four…

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Q: WXYZ is an isosceles trapezoid with bases WZ and XY and midsegment MN. Use the given information to…

A: Tarpezoid mid segment theorem Theorem: The midsegment of a trapezoid is half the lengths of the two…