At what point does the normal to y = 2x2 – (3 + 2x) at (1, –3) intersect the parabola a second time? Answer: Note: You should enter a cartesian coordinate.

Q: At what point does the normal to y = 2 + 2x + 2x² at (1,6) intersect the parabola a second time?

A:

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

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: Find the slope of the tangent to the parabola y=x^2 at x=1 a. 1 b. 2 c. 3 d.4

A: The slope pf the parabola = 2

Q: ive the Normal Equations to fit the parabola y = a + bx + cx².

A:

Q: At what point does the normal to y=4x2−(2+3x)y=4x2−(2+3x) at (1,−1)(1,−1) intersect the parabola a…

A:

Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Find an equation of the normal line to the parabola y = x – 9x + 5 that is parallel to the line x -…

A:

Q: Find the equation of the tangent plane to the surface - 8x3 + 7y³ + 3xy at the point (2,0, 64).

A:

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

A:

Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

A:

Q: Find an equation of the normal line to the parabola  y = x2 − 4x + 1  that is parallel to the line…

A:

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

A:

Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

Q: How far from the y-axis is the center of the curve 2x2 + 2 y² + 10x – 6y – 55 = 0? %3D 2.50

A:

Q: 3. Find the line normal to the ellipse at X=-1 y= 2+4x-x3

A: Given, y=2+4x-x3 At x= -1 y=2+4-1--13y=2-4+1y=-1 Now point -1,-1

Q: Find the equation of the sphere if one of its diameters has endpoints (3, -4, 5) and (5, 0, 11)…

A:

Q: Find the equation of the plane tangent to the surface of Z= x2+ Y2 at point P(125)

A:

Q: At what point does the normal to y = 3x – (5 + 4x) at (1, –6) intersect the parabola a second time?…

A:

Q: Where does the normal line to the parabola y= x- x2 at  the point (1, 0) intersect the parabola a…

A: Normal to a curve is a line which is perpendicular to the curve at its point of intersection with…

Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A:

Q: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

A:

Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: Find the point on the curve y = Vx closest to the point (1,0).

A:

Q: ind the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

A:

Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

A:

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Find the equation of the normal line to the parabola y = x + 3x – 2, that is also parallel to 7x…

A:

Q: Find the equation of the tangent and normal to the parabola y=4ax at the point (at²,2at)

A:

Q: Find the equation of the sphere if one of its diameters has endpoints (3, 1, -5) and (5, 5, 1) which…

A:

Q: Given the parabola: x2+12y=0 and the tangent line x+y-3=0, find the point of tangency

A:

Q: Determine the equation of the normal line to the hyperbola x - 4y- = 9 at (5, 2). 8x + 5y – 50 = 0…

A: Given equation of hyperbola is  x2-4y2=9          ...(1) We have to find the equation of the normal…

Q: Find the equations of the tangent and normal to the parabola y² - 2x - 4y -1 = 0 at the point (-2,1)

A:

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

A:

Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

A:

Q: Exer. 35-36: Find equations of the tangent line and normal line to the hyperbola at the point P. 3…

A:

Q: 3x + xy? 2y + x?y dy dx

A:

Q: Find an equation of the normal line to the parabola y = x2 - 8x + 9 that is parallel to the line x -…

A:

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: 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: 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: Determine the equation of the normal line to the hyperbola x^2 - 4y^2 = 9 at (5,2)

A: We have to find equation of normal

Q: Find the point on the graph of z = (x² + y)? at which the tangent plane is parallel to the plane 2x…

A:

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: Determine the equation of the normal line to the hyperbola x2 – 4y2 = 9 at (5, 2).

A:

Q: Compute y ds over the part of the parabola y =2Px, for P > 0 starting at (0,0) at (2P,2P).

A:

Q: Find the equation of the line through the origin auel normal to the line x=y-S,2:2y-3?

A: Let ,     L1 : x-01=y-51    L2 : y-321=z-02L be the required line which passes through 0,0,0 &…

Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

A:

Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

A: