3- The parabola y= ax'+bx+e, mean that the equation y ax' is . .........

Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

A:

Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

A:

Q: 5. Find the equation of the tangent line that passes through point (1,2) to the graph 8y3 + x²y – x…

A: Proceed as shown below...

Q: Determine the orthogonal trajectories of the hyperbola 3xy= 5 at the point (2, 5/6). Sketch the…

A:

Q: 4. At the point (0, 0) the graph of y 4.x2 has greater curvature than does y 2x2.

A: These equation represents parabola,then Radius of curvature: K=  y'' /([1+(y')²]^3/2)

Q: 3. Find the differential equation of a family of parabolas with axis parallel to the x-axis.

A:

Q: What is the equation of the line tangent to the parabola y2=12x at point (2,2)

A: y2=12x  ⇒  4a=12                     a=3

Q: 5. Find the equations of the tangent line and normal line to the parabola y = 2x² at the point…

A: Since, you have asked multiple questions , according to our guidelines we are supposed to answer…

Q: How do you find the equation of the tangent line to the parabola for y = x2 − 3x − 1 at x = 4.

A: The equation of the given parabola is y=x2-3x-1. We have to find the equation of the tangent line to…

Q: Find the formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

Q: Sketch typical solution curves in the regions in the xy-plane determined by the graphs of the…

A: Given: f(y)=y2(9−y2)  To find: Solution

Q: 8. At what point of the parabola is the tangent line parallel to 7x+y-2=0? y = 2r-3x +1 O (1,0) O…

A: Here is the solution:

Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: Find the differential equation of the family of hyperbolas having center at C(0, k), whose…

A: First write the standard equation of hyperbole having transverse axis parallel to y-axis and satisfy…

Q: Obtain the differential equation of the family of circles having their centers on the x-axis.…

A:

Q: The slope of the tangent line to the parabola y 2x + 3x +6 at the point (1, 11) is: The equation of…

A:

Q: Find the parabola with equation y = ax2 + bx whose tangent line at (1, –1) has equation y = 3x – 4.…

A:

Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

A:

Q: Find the parabola with equation  y = ax2 + bx  whose tangent line at  (1, −1)  has equation  y =…

A:

Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

A:

Q: At what point of the parabola y = x² – 3x – 5 is the tangent line parallel to 3x - y = 3? O (-3,-5)…

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Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

A:

Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: The slope of the tangent line to the parabola y 2x2 + 2x + 4 at the point (0, 4) = The equation of…

A:

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

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Q: Obtain the differential equation of the family of circle with center on the x-axis

A:

Q: Two children weighing 16 and 24 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

A: Given,           Two children weighing 16 and 24 kilograms are sitting on opposite sides of a…

Q: The line y = 2x - 9 is tangent to the parabola y = x'2 + ax + b at the point (4,-1). What are the…

A: Given y=2x-9 is tangent to y=x2+ax+b at (4,-1) So, y=x2+ax+b passes through (4,-1)Put x=4 and…

Q: What are the order and degree of the differential equation representing the family of parabolas y2 =…

A:

Q: The slope of the tangent line to the parabola y 3x? + 2x + 3 at the point (– 5, 68) is: The equation…

A:

Q: 2-g(%,y)%3D플-플 * at (VT ,1)

A:

Q: Haw J Express the fallasing function by Cartesian equationst 3K34tane Seco

A:

Q: Determine the differential equation of all circles whose center is on the y-axis.

A: Solution...

Q: (a) Where does the normal line to the ellipse x2- x   y + y 2 = 3 at the point (1, -1) intersect the…

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Q: 11. Show that the tangent to the hyperbola x-y = 1 at the point P(coshu, sinhu) except when vertical…

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Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: Find equations of both tangent lines to the graph of the ellipse x2/4 + y2/9 = 1 that pass through…

A: We have given equation of curve x24+y29=1 and point 4,0 We will find slope of tangent at any point…

Q: 2. Find an equation of a curve satisfying the ff. condition and passing through the point (0, -1).

A: dxy-dy1+x3=0A first order separable ODE has the form of Ny·y'=MxLet y be the dependent variable.…

Q: 17. The line with equation y = 2x b where bis a constant, passes through the point (3, 6). What is…

A: When a line passes through a point then the coordinate  values of the point must satisfy the…

Q: Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at (-2,6)…

A: solve the given problem.

Q: find the differential equation of circles with center on the y-axis

A:

Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

A:

Q: Find the orthogonal trajectories of the families of Parabolas y a + 8az + 16a, which passes through…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.