The area of the triangle formed by the tangent and the normal to the parabola y = 4ax both drawn at the same end of the latus rectum and the axis of the parabola is

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 area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

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

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Q: 2x +3K Zx2 - 4x + 13

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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: A circle with radius 1 centered at (0, ) is tangent to two points of the parabola y = a². What is…

A: We have to find the area of the shaded region.

Q: Find a formula for the distance from the point P(x, y, z) to the y-axis.

A: Given : The point is P ( x , y , z ) to the y - axis .

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: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: Find the arclength of y = 2x2/3 from x is greater than or equal to 1 and less than or equal to 2

A: The arc length of the function y=2x23 between x=1 to x=2.

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

A: Find the distance using distance formula and then differentiate to get the minimum value equate 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: 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: If the infinite curve y = e-6x, x > 0, is rotated about the x-axis, find the area of the resulting…

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Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

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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…

A: We have to calculate the area of the smaller region bounded by x+52=2y from left sides,and bounded…

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

A: Introduction ::

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

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Q: Prove that the product of the perpendicular distances F1R1 and F2R2 from the foci to a tangent line…

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Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

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Q: Let LL be a tangent line to the hyperbola xy=8 at x=7. Find the area of the triangle bounded by L…

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Q: Find the length of the arc of the parabola y²=4x from the vertex to a point where x=4.

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Q: Find the length of the tangent to the circle x² + y² − 2x − 3y − 1 = 0 from the point (2, 5)

A: Solution- The equation of the circle x2+y2-2x-3y-1=0 The point =2,5 length of the tangent

Q: Find the least radius of curvature of the cubic parabola y=x3.

A: Given To find the radius of curvature, first find the curvature (K) using the formula. Find the…

Q: a) Show that the length of the arc of parabola y? =16x measured from the vertex to an extremity of…

A: Given the parabola y2 = 16x.

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

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

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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: What is the maximum vertical distance between the y=x+2 and the parabola y=x^2 for -1 is less than…

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Q: b. the length of the tangents from the point (2, 5) to the circle x +y² -14x-2y+34= 0

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Q: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

Q: The region in the first quadrant bounded above by the parabola y = x ^ 2 below by the x -axis, and…

A: Follow the steps.

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

A: Consider the circle, x2+y2=25 find the equation of the tangent line,…

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: Find the area of the surface of revolution generated by revolving about the x-axis the arc of the…

A: y2=12x ⇒y=23x ⇒dydx=3x ⇒dydx2=3x2 ⇒dydx2=3x ⇒1+dydx2=1+3x ⇒1+dydx2=1+3x

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

A: Solution of the problem as follows

Q: The maximum vertical distance between the parabola y = 3-z and the line y = 3x+2 on the interval…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: