3. Use the distance formula to prove that the point (4,2) is on the parabola x = Sy. Prenared hu

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

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Q: Show that the square of the length of subtangent at any point on the curve by2=(x+a)2 (b is not…

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Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

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

A: Given that x23+y23=a23 To find the length of the curve:…

Q: 5. What is the maximum vertical distance between the line y = x + 2 and the parabola y = x² for – 1…

A: The given equations are, y = x + 2       ....(1)  y = x2            ....(2) To find the maximum…

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Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: Find the length of arc of the curve 9y^2=4x^3 from the origin to the point (3,2 squareroot of 3)

A: The arc length of a curve y=f(x) from x=a to x=b is defined by the integral L=∫ab1+dydx2dx.

Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: 9. Prove, by coordinate geometry that QRST is a parallelogram. Q(0

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Q: (b) Prove that the perpendicular bisector of a chord of a circle passes through the centre.

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Q: Find the minimum distance from the parabola a – y? = 0 to the point (0, 3). Minimum distance =

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Q: 2. Evaluate dy, where C is the part of the parabola y = x² from (1, 1) to (2, 4).

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Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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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: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

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Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

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Q: Show that the square of the length of the subtangent at any point on the curve by2=(x+a)3 (b is not…

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Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 when x = 5? a = b…

A: Given: The line 4x+y=b is tangent to the parabola y=ax2 when x=5. To Find: Value of a and b.…

Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

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Q: 16)- Consider the quadrature formula 6 | f(x)dx = Af (-6) + Bf(6) -6 If the degree of precession is…

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

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

Q: If PP' is a diameter of the rectangular hyperbola xy = c' show that the locus of the intersection of…

A: given , if PP' IS a diameter of the rectangle hyperbola xy = c^2  show that the locus of the…

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: Find the area of the segment cut off from the parabola x2 = 8y by the line x- 2y + 8 = U. %3D

A: Introduction ::

Q: What is the minimum vertical distance between the parabolas y = x² + x en y = x – x²?

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Q: Show that the square of the length of subtangent at any point on the curve by 2 = (x+a)3,(b is not…

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Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

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Q: Sketch the solid described by the given inequalities. 3sps 4, os ps a/3, 0S0SR 1.5 21.0 0.5 00…

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Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

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Q: On the bisector of the second and fourth quadrant determines a point p such that the sum of the…

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Q: Prove that the midpoint of the hypotenuse of a right triangle is. equidistant from the verticle

A: Instead of T,S,V and M I choose C,A,B and D

Q: And the eguation of lines in which the blane 2x+47280 4u2-y2= 32²=0. ーザ cuts the cone Also find ind…

A: Hi! You have posted multiple sub-parts. As per norms, we will be solving only three sub-parts. We…

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: Solve the following problems completely. If there are seven distinct points on a plane with no…

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Q: Use the method of Lagrange to show that of all the triangles inscribed in a fixed circle, the…

A: Let the sides of the triangle are a+b,b+c,c+a    a,b,c>0 s(Semi-perimeter)= (a+b) +(b+c) +(c+a)…

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

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Q: The semi-hyperbola H(X)=(sqrt(x^2-1)) is continous at which x interval?

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

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

Q: Use the side-splitter theorem to solve for a in the triangle below. 8 6.

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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: 3. Find the shortest distance from the origin to the plane x – 2y – 2z = 3. |-

A: Here I am attaching image so that you understand each and every step.

Q: Consider the parabola f (x) = x² – 4x and the line g(x) = –2x – 1. Determine the %3D point(s) of…

A: Given parabola,y=x2-4x                     (1)Given line y=-2x-1                     (2)Put value of…

Q: 17) - Consider the quadrature formula ²₁ f(x) dx = f(-²) + ‡ƒ (²) If the degree of precession is 1,…

A: Consider the given quadrature formula, ∫-11fxdx≅45f-12+65f13 Here it is given that degree of…

Q: Which of the following points do not lie on any tangent line of the parabola y = x2 + 2? (2,6) O…

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Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: Find a number k such that the line y=6x+4 is tangent to the parabola y= x2 + k.

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