Given the point P =,(a,b) in the first quadrant, find the downward-opening parabola that passes through the point P and the origin such that the area under the parabola is a minimum. (Hint: a parabola is defined by three points.)

Q: Let L be a tangent line to the hyperbola xy = 8 at x = 9. Find the area of the triangle bounded by L…

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Q: find the radius of curvature at any point on parabola y2=4ax

A: Given:  y2 = 4axTo find: The radius of curvature at any point on the given parabola. Formula used:…

Q: Find the radius of curvature at any point on parabola y2=4ax

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Q: Let L be a tangent line to the hyperbola xy=4at x=7. Find the area of the triangle bounded by L and…

A: Given: L is a tangent line to the hyperbola xy=4 at x=7. To determine: The area of the triangle…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

A: Please see the below picture for detailed solution.

Q: Find the area of the resulting surface if an arc of a parabola y = x? from (1,1) to (2,4) is rotated…

A: Given curve is y=x2

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2=2y, the…

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Q: write the equationns of the curves enclosing a reigon such that when it is rotated aboutthe x-axis,…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2=2y, the…

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Q: Find the area of each of the following surfaces.   The portion of the sphere with equation x 2+y 2+z…

A: Given, x2+y2+z2=16 , lies inside  x2+y2=9 surface area =2∬1+zx2+zy2dxdy…

Q: Let L be a tangent line to the hyperbola xy 32 at x3 Find the area of the triangle bounded by L and…

A: Find the equation of the hyperbola,

Q: Find the minimum distance from the point (2, 4, 10) to the paraboloid given by the equation z = x +…

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Q: Find the asymptotes of the cissoid of Diocles defined by the equationy2(2a−x)=x3,a>0.

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Q: The base of a solid is the region in the first quadrant between the graph of y and the raxis for 0<…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y, the…

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Q: A flashlight shape like a paraboloid has its light source at the focus located 1.5cm from the base…

A: Sol:     given:  4 flashlight shape like parabolaod                  and its light source of the…

Q: What is the ratio of the area to the perimeter of an ellipse 9x² + 25y² = 225? %3D O None of these O…

A: Topic:- geometry

Q: What is the DE of the family of parabolas having their vertices at the origin and their foci on the…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y, the…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

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Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

A: Please see the below picture for detailed solution.

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: Use Green's theorem to find the area between ellipse 16 = 1 and circle x2 + y2 = 25.

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…

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Q: Find the value of c>0c>0 such that the area of the region enclosed by the parabolas y=x^2−c^2 and…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)2=2y, the…

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Q: Find the area of the parabala : z-2x*+ 2,² that lies between the levels z=¢ and z=2. To do this,…

A: Given the equation of the parabola z=2x2+2y2 that lies between the levels z=12 and z=2

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: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

A: Surface area

Q: The centroid of the area bounded by the parabola y^2 = 4ax and the line x = p coincides with the…

A: Please see the attachment

Q: No. of integral points lying inside the parabola y² = 8x and circle x? + y? = 16 are %3D (A) 15 (B)…

A: To find  The number of integral points lying inside the parabola y^2=8x and the circle x^2+y^2=16.

Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)²=2y, the…

A: Find the slope of the tangent to the curve x2+y2=25 at (3,4). 2x+2ydydx3,4=0dydx3,4=-xydydx3,4=-34

Q: Is it possible to angle the flashlight in such way that the boundary of the lighted area is a…

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Q: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)² = 2y, the…

A: The shaded region is our required area

Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: If a chord of the parabola y? = 4ax is a normal at one of its ends, show that its mid-point lies on…

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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: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

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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: Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)2 = 2y, the…

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Q: Find a parametrization of the osculating circle for the parabola y= X sequar when x=1

A: The given equation of parabola is y = x2.We are asked to find the equation of osculating circle for…

Q: Find the length of the arc of the parabola x² 4ay measured from the vertex to one extremity %3D of…

A: We can calculate the length of arc using given condition and  formula of length of arc

Q: - Show that the distance r from the origin O to the point P(Coshu,Sinhu) - on the hyperbola x-y 1 is…

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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: 13. Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y,…

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Q: Prove that the surface area of a sphere with radius r is given by S = 4r? using the methods of this…

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Q: QUESTION 9 Calculate the area of the smaller region (to the left of the parabola) bounded by (x+5)…

A: Please see the below picture for detailed solution.

Q: A circle with radius 1 centered at (0,) is tangent to two points of the parabola y = ². What is the…

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