Find points P and Q on the parabola y = 1 – x² so that the triangle ABC formed by the x- axis and the tangent lines at P and Q is an isosceles right triangle P B C

Q: Let the curve C be the mirror image of the parabola y" the line x+y + 4 = 0 If A and B are the…

A: Given: Parabola:y2=4xLine:x+y+4=0   A and B are the points of intersection of C with the line y=−5…

Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: The tangent of the parabola x = y² + y + 1 at the point (1,0) is

A:

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

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 the exact length of the curve. x = et – t, y = 4et/2, 0st < 5

A: Find the length of curve:

Q: A] Find the length of the arc of the semi-cubical parabola y2 x (1,1) and (5,5V5). 8250 between the…

A: Solution:Given        y2=x3    between the points (1,1) and (5,55)To find the Arc…

Q: Cоmрute (x + y) dz, where is the portion of the parabola C y = 4 – x2 from -2 to 1+3i.

A:

Q: Find the exact length of the curve. x = et + e-t, y = 5 – 2t, 0 st< 4

A: Given curve: x=et+e-t, y=5-2t We have to find exact length of the curve at 0≤t≤4. Length of the…

Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

A:

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: Find all hyperbolic lines that passes through i +1 and parallel to the y-axis.

A: Find all hyperbolic lines that passes through i+1 and parallelto the y-axis.

Q: Find the midpoint of these two points (4, 6) and (7, 10) Use the formulas: x = (x1 + x2)/2 %3D y (yi…

A: Consider the points, 4,6      and         7,10 The midpoints of two points is given by the formula,…

Q: Let P(x1, y1) be a point on the parabola r? = 4py, p> 0, with focus F(0, p). Let a be the angle…

A:

Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

A:

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: - Find the equation of the tangent to the circle x2 С. Зх + 5y + D. Зx - 5y + А. Зх + 5y -34%3D0 B.…

A: Find the equation of the tangent to the circle x² + y2 - 34 = 0 through (3, 5).

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

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: Find the exact length of the curve. y2 = 16(x + 3)3,   0 ≤ x ≤ 3,  y &gt; 0

A: Given: Find the exact length of the curve.

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: The plane x = 1 intersects the paraboloid z = x2 + y2 in a parabola. Find the slope of the tangent…

A: Given that the plane x = 1 intersects the parabolic z = x^2 + y^2 in a parabola.   So,…

Q: 1. Let P(r1, y1) be a point on the parabola r? be the angle between the parabola and the line…

A: angle with a curve at a point means angle with tangent line at that point of curve .

Q: Given the parabola y=2x2. A secant is drawn through the 2 points of the parabola, which have the…

A: Basic strategy for this question is that we will find the slope in two ways and then equate them to…

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

A:

Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

A:

Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

Q: 4 Find a. the equations of the tangents to the circle x +y + 4x – 2y – 24 = 0 at the points where…

A:

Q: Find the tangent plane to the equation z = - 3x² + 2y² + 4y at the point (4, 1, - 42). 2 = Check…

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

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

A:

Q: 2. Find points P and Q on the parabola y = 1 – x? so that the triangle ABC formed by the r-axis and…

A: Given:  To find points P and Q on the parabola y=1-x2 so that the triangle ABC formed by the x‐axis…

Q: 5 B 6. 8. A A) Tangent B) Not tangent

A: To determine whether AB is a tangent to the circle  Let the centre of the circle be O and point on…

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

A:

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

A:

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

A:

Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y &gt; 0

A:

Q: For the curve given by r(t) = (8sin(t), -3t, -8cos(t)), find the unit tangent.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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

A:

Q: (a) Prove that curves a, ß: I → R² are congruent if k̟ = Kg and they have the same speed.

A: Part (a):   If any two continuous function defined on the interval I, and the two curves are…

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: 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: Evaluate S,lz| dz for the curves C1 and C2, both of which begin at a = 1 and end at b = -1. The…

A:

Q: 1. Let P(x1, Y1) be a point on the parabola x?: be the angle between the parabola and the line…

A:

Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

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: 2. Find the equation of the tangent to the circle x2 + y2 +4x +16y - 32 = 0 through (4, 0).

A: